For Samsung, the South Korean behemoth whose name means “three stars,” 2016 will go down as a decidedly one-star year.

As if the embarrassing cancellation of its Galaxy Note 7 phone and its convoluted ­efforts to keep the company in family control weren’t difficult enough, the year has finished with Lee Jae-yong, the company’s heir apparent, being grilled by lawmakers over his possible involvement in the sensational political scandal that is rocking South Korea.

“Samsung is facing the greatest challenge since its foundation 60 years ago,” said Kim Sang-jo, professor of economics at Hansung University and an expert on conglomerates, or chaebol, as they are known here.

As many as 500 Samsung Electronics executives started a three-day meeting Monday to review the last six months and discuss business strategies for 2017.

It’s hard to overestimate the influence that this conglomerate has in South Korea, which is sometimes referred to as “the Republic of Samsung.” The company sells everything from life insurance to ships to refrigerators, has businesses that include construction and advertising, and runs an amusement park, hotels and hospitals. The group’s assets are equal to one-fifth of South Korea’s gross domestic product.

But now, just like the real republic, Samsung is in a state of turmoil.

“I am embarrassed to be involved in this incident,” Lee, the grandson of Samsung’s founder, told lawmakers this month during an unprecedented 13-hour hearing. “We should have been a better example as a South Korean company.”

The leaders of the country’s top nine chaebol were questioned about their donations to two foundations run by Choi Soon-sil, a secret confidante of President Park Geun-hye. Prosecutors allege that the chaebol donated almost $70 million to win business favors, and that Choi then embezzled it.

The National Assembly voted to impeach Park this month over the scandal, suspending her from her duties while the country’s top court considers whether to uphold the motion.

[ South Korea’s parliament votes to impeach president over corruption scandal ]

Samsung has been stuck in something of a power vacuum for the last 2½ years, since Lee Kun-hee, the 73-year-old chairman of Samsung Electronics and the son of the founder, had a heart attack. He remains hospitalized. Samsung won’t comment on his condition, but media have reported he is in a coma.

Lee Jae-yong, the third-

generation heir apparent, is officially still vice chairman but is effectively running the company.

A 48-year-old who likes to be called Jay, Lee has been groomed to succeed his father. He speaks fluent English and Japanese and graduated from prestigious universities in Seoul and Tokyo. He began a doctoral course at Harvard Business School but left before completing it.

However, the Lee family faces significant problems in maintaining its hold. Family members own only a tiny fraction of the shares but control the conglomerate through a complex web of cross-shareholdings.

Simply transferring Lee Kun-hee’s equity to his children upon his death would cost them billions of dollars in inheritance tax. Instead, the family appears to be trying to keep control by splitting and merging key units of the conglomerate, analysts say.

It tightened its grip last

year when the conglomerate’s de facto holding company, Cheil Industries, of which Lee Jae-yong is the largest shareholder, merged with Samsung C&T, a construction arm.

International investors, led by a New York-based hedge fund, opposed the merger and had been pushing for restructuring, but the National Pension Service, a major shareholder, supported it.

[ Scandal shows that ‘Korean disease’ of corruption is far from cured ]

Outside investors have long railed against the byzantine ownership structures at South Korea’s conglomerates but have had little success in changing them because of shareholdings that give the controlling family outsize power.

Prosecutors now allege that Samsung paid $26 million in bribes to Choi, the president’s confidante, and that she in turn put pressure on the pension fund to back the deal.

Prosecutors have raided the offices of the pension fund, Samsung and other conglomerates that are believed to have made payments to Choi’s foundations. The cases have renewed attention on the ­decades-old links between the president’s office and the chaebol, which were promoted by Park’s father, who was president of South Korea in the 1960s and 1970s.

At the hearing, Lee said that the merger made good business sense and denied any involvement in a bribery scheme. He did, however, admit that Samsung had given a $900,000 horse to Choi’s daughter, an equestrian.

Samsung, meanwhile, is grappling with the fallout over the cancellation of its Galaxy Note 7, a smartphone that was meant to rival Apple’s latest iPhone but had an annoying habit of catching fire.

The company had to recall all the phones, which are now banned on most airlines, and terminated the line after being unable to determine the cause. The fiasco inflicted a $5.3 billion blow to Samsung’s balance sheet.

The company is “carefully revisiting every aspect of the device, such as its hardware, software and manufacturing processes,” that could have caused the problem, said spokeswoman Rhee So-eui.

To try to put out the institutional fire, Samsung recently said that it would consider dividing itself into a holding company and an operating company — a key demand of those seeking better corporate governance — over the next six months and that it would ­increase this year’s dividend ­payments to shareholders by 30 percent.

It also said it would consider listing its shares on an American stock exchange.

“Today’s announcement extends the actions we initiated last year and represents the next phase in the evolution of our shareholder policy and governance,” Kwon Oh-hyun, vice chairman and chief executive of Samsung Electronics, said in a conference call.

[ South Korea’s political crisis could become a trigger for bigger change ]

But analysts said that Samsung was still operating as chaebol always have — relying on cozy links with the government to create a favorable business environment.

“It’s time for Samsung to adopt global standards,” said Kim of Hansung University, urging more transparency within the conglomerate. But he cast doubt on Samsung’s plans and said the current political upheaval — it could take six months for the courts to rule on Park’s impeachment — was not helping. “It’s difficult to predict the directions of the country because it’s unclear who will be the next president,” Kim said.

Doh Hyun-woo, an analyst at Mirae Asset Global Investment, said it was inevitable that Samsung would have to change. “Other conglomerates have already begun the process of changing their structure, and Samsung needs to go down that path, too,” he said.

For now, Samsung is hoping that it can rescue its reputation — and its revenue — with a new phone, one that doesn’t have a propensity to explode.

“Samsung is expected to launch a new mobile phone in March next year, and as far as I know, the company is doing its best not to have any problems,” Doh said. “I think Samsung will be able to recover from this tough year soon.”

Samsung has a good track record when it comes to renewal. In 1993, when Samsung Electronics was still associated with cheap, inferior products, Lee Kun-hee famously exhorted his employees: “Change everything except your wife and kids.” They did.

Yoonjung Seo contributed to this report.

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