Mike Burley/Topeka Capital-Journal, via Associated Press

Charles and David Koch preside over a vast private empire that manufactures a dizzying array of products, from oil pipelines to Brawny paper towels.

On Monday, the brothers’ conglomerate made a big move into a very different business by offering to buy Molex, a relatively obscure maker of electronics plugs for the likes of Apple — for $7.2 billion.

Related Links Document: The press release

The deal, the biggest by Koch Industries in eight years, will give the two control of a company whose products reside in computers, X-ray machines and even the iPhone 5.

The transaction trails only Koch Industries’ roughly $22 billion takeover of Georgia-Pacific in 2005. But it may signal that the conglomerate is on the prowl for more opportunities.

Earlier this year, Georgia-Pacific agreed to buy Buckeye Technologies for $1.45 billion. And another Koch subsidiary invested $240 million in a management buyout of American Greetings, the greeting card maker.

The billionaire brothers have said publicly that they aspire to transform Koch Industries into something like Berkshire Hathaway, the conglomerate run by Warren E. Buffett, whose varied holdings include the Burlington Northern Santa Fe railroad company and half of H. J. Heinz.

Mark Lennihan/Associated Press

Under the terms of the deal, Koch will pay $38.50 a share. That is a 31 percent premium to the Friday closing price for Molex’s common stock and a 56 percent premium to its Class A shares.

A significant portion of those proceeds will go to the Krehbiel family, whose development of a new kind of plastic gave birth to Molex, which generated $3.6 billion in sales and $243.6 million in profit in its most recent fiscal year.

Molex was born in 1938, when Frederick A. Krehbiel and his son Edward sought to take advantage of their new invention. Among its initial uses was the manufacturing of flowerpots and clock cases.

The entrance of John H. Krehbiel Sr., another son, prompted the company to begin focusing on making electrical connectors for appliances, including stoves by General Electric and freezers by Whirlpool. (The latter still uses Molex products.)

That business increasingly began to take up more of Molex’s operations, enough that the company created an international division in 1967 to work with Japanese electronics manufacturers.

But in recent years, Molex has struggled to improve its operations, including lifting its margins. It also drew scrutiny for a number of problems, including accounting issues that led to the departure of Deloitte as its auditor and, later, the improper backdating of stock options.

The Krehbiel family turned to Byron D. Trott, a former rainmaker for Goldman Sachs who has since set up his own advisory firm, to quietly explore a sale of the company, according to a person briefed on the matter.

Among the potential buyers that Mr. Trott contacted was Koch, whose controlling brothers zealously guard their company’s privacy. Analysts say that under private ownership, Molex will free itself from the burdens of being a publicly traded company.

“After 75 years, this was a difficult decision, but our board of directors and our family believe that this transaction, which follows a diligent and thorough review process by the board, provides outstanding benefits for all our stakeholders,” Fred Krehbiel, Molex’s chairman and a 72-year-old grandson of the company’s founder, said in a statement.

Based in Lisle, Ill., Molex had 35,983 employees as of June 30. When its sale closes, expected by year’s end, the business is expected to operate as an independent subsidiary of Koch Industries.

Selling the company to private owners could also buy Molex time to improve its operations. The Koch brothers have little need to generate a profit immediately: Forbes magazine estimates that Charles and David Koch are each worth about $34 billion.

“Molex has become a global leader by focusing on product innovation and value creation, driven by its talented leadership and employees,” Charles Koch said in a statement. “We look forward to jointly applying the capabilities of our two companies to help take both to the next level.”

Molex’s new owners may shy from publicity, but they are no strangers to controversy. The brothers’ political advocacy and donations to conservative groups has drawn sharp criticism from liberals. President Obama himself has cited the pair for their work financing opposition to his policies.

The Krehbiels are also politically active, albeit on a far smaller scale. Fred Krehbiel donated an estimated $281,650 to politicians and advocacy groups over the last three election cycles, according to OpenSecrets.org. Most of the recipients were Republican candidates, including Senator Mark Kirk of Illinois and Senator Rob Portman of Ohio.

Fred Krehbiel’s son, Liam, is chief executive of A Better Chicago, an organization that helps finance nonprofits in that city.