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There are groundbreaking business deals. And then there are ones that threaten to break up governments.

When Denmark gave the global financial giant Goldman Sachs the go-ahead on Thursday to buy a stake in its state utility, the move was not exactly followed by a celebratory signing ceremony.

So divided was the Socialist People’s Party that it withdrew its ministers from the country’s governing coalition. Some party members said the deal ceded too much power to Goldman. Annette Vilhelmsen, the party’s leader, who supported the deal, stepped down from her leadership role since she could not reach agreement within her party.

The party’s withdrawal from the coalition left the government of Helle Thorning-Schmidt, the prime minister, with a tenuous grip on power.

That so many Danes have been aghast at the idea of giving Goldman Sachs a prominent role in the country’s energy future reflects how far the damage to the investment bank’s reputation has spread since the financial crisis.

However much the financial world might envy Goldman’s trading prowess, many Danes see Goldman as an emblem of an industry that helped cause the crisis and then profited handsomely even as much of the Continent still struggles to recover.

Thousands of people have taken to the streets in recent weeks to protest the deal; a prominent banner featured the vampire squid that critics have come to embrace as a symbol of Goldman Sachs. Nearly 200,000 Danes signed an online petition against the deal, a record.

The deal was approved on Thursday by a parliamentary committee. The departure of the Socialists left the two remaining parties in a precarious position.

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But Prime Minister Thorning-Schmidt, who is best known internationally for her recent “selfie” with President Obama at the funeral of Nelson Mandela, said she would form a new government. The two remaining parties in the coalition government, her Social Democrats and the Social Liberal party, hold about a third of the seats in the Parliament. The Socialists said they would still support the coalition in parliamentary votes. The governing coalition is also backed by a far left party.

“It is quite an odd day in the Danish Parliament, considering one of the three parties that was in the government has left,” Benny Engelbrecht, a Social Democratic lawmaker, said in an interview. He said the departure of the Socialist People’s Party “was over a number of things, but inspired by this.”

“In Danish, we have an expression, ‘The drop that makes the glass spill over,’ ” he said, “and this was what made the glass spill over.”

Under the terms of the deal, Goldman would invest about $1.45 billion for an 18 percent stake in Dong Energy, the state utility, which has become a green energy exemplar in its push for electricity from wind turbines. Though the deal buys far from a controlling share, the minority stake would come with special privileges.

Goldman would get a seat on the utility’s board. And the bank, along with two Danish pension funds, would have veto power over changes in the utility’s strategy or its executive suite — specifically the utility’s chief executive or chief financial officer. The Danish pension funds are investing about $550 million.

Among the questions about the deal is whether it is being structured to avoid taxes. Goldman’s investment will be made through a company based in Luxembourg. Danish Broadcasting has reported that shares in the Luxembourg company are partly owned by entities based in the Cayman Islands and Delaware.

In a statement, Goldman Sachs said it “complies, and will continue to comply, with all applicable tax laws in Denmark, Luxembourg, the United States and other relevant jurisdictions.” A Cayman Island partnership was set up primarily for investors outside the United States and a Delaware partnership was for investors in the United States, Goldman said.

Goldman expressed its “long-term commitment” and its support for the current management and its strategy, which the bank said included “significant renewable energy investments.”

Dong Energy has a number of businesses, but it is perhaps best known of late for its leading role in building offshore wind farms. Dong also drills for oil and gas in the North Sea, has about one million gas and electric customers and operates coal and biomass power plants.

Karsten Anker Petersen, a Dong spokesman, said building wind farms “requires huge investments upfront, and that’s part of why we need the capital injection from our new investors.”

Goldman has a long history of buying up or investing in big public infrastructure companies and projects, and it manages investment funds dedicated to those efforts. In 2010, it bought a Spanish natural gas distribution network. This month, one of its funds sold its stake in SSA Marine, a global port operator.

There has been no shortage of Danish ire about the deal. In an editorial, Berlingske, a national newspaper, has argued that “Goldman Sachs might send a lot of its earnings from the investment to the Cayman Islands to avoid Danish taxes.” It added, “This happens at the same time the Danish government is fighting against exactly this type of tax evasion.”

On Wednesday, an estimated 4,000 people gathered in front of Parliament to protest the deal. A few supporters also turned up, including Rasmus Jarlov, a member of the Copenhagen City Council and the Conservative Party.

During an interview, he was hit by a snowball, and later, he and three other conservatives were attacked by protesters.

An earlier plan to make a public offering of stock in 2008 was abandoned during the financial crisis. Under the current deal, Goldman and the Danish pension funds will be able to sell their shares back if there is not a public offering by 2018.

Supporters said Goldman had offered the best deal. Mr. Engelbrecht, the parliamentarian, who voted for the deal, said: “I’m not interested in being a shield for Goldman Sachs — they’ve done a lot of crazy things over time with regards to the financial crisis. They’ve got a bad reputation, no doubt about that.”

But he added, “Now they support green growth and green energy, which is something I’m quite proud of. That someone as focused on revenue as Goldman Sachs thinks green growth and green energy, especially wind energy, holds big potential for the future.”