(Reuters) - General Motors Co GM.N shareholders on Tuesday overwhelmingly rejected proposals by hedge fund Greenlight Capital to restructure the company's stock and reshape its board, backing Chief Executive Mary Barra's efforts to rev up the company's stalled share price.

Fending off the challenge from Greenlight founder David Einhorn does not mean the end of Barra’s battles. GM shares traded on Tuesday at $34.25, about 16 percent lower than when Barra became CEO, despite robust profits and a series of moves to sell or shut down money losing operations.

The win also does not mean pressure will let up from Greenlight, which is the fifth largest shareholder, and while gracious in defeat, continued to make the case for fresh faces on the board.

“We are disappointed that shareholders have elected to maintain the status quo,” Einhorn said in a statement on Tuesday. “We congratulate GM’s management on their win today.”

Greenlight’s campaign came as U.S. auto industry sales of new vehicles have begun to wane after a boom cycle that has lasted since 2010.

Silicon Valley electric vehicle maker Tesla Inc TSLA.O this year surpassed GM's market value, reflecting investor confidence that, despite heavy losses, Tesla has a better strategy as the auto industry shifts to ride services and electric, autonomous vehicles.

In comments before Tuesday’s shareholder meeting, Barra acknowledged Greenlight’s position on its stock price, saying “we do believe GM stock is undervalued,” and said the company “is continually looking at ideas” to increase investor interest.

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Preliminary results showed more than 91 percent of shareholders voted against Greenlight’s proposal to have GM offer dividend and capital appreciation shares, according to GM officials at the meeting.

GM’s board nominees were elected with between 84 percent and 99 percent of the vote, the company said. The board will remain the same at 11 members, with Barra as chairman.

Einhorn floated the dual-class proposal in March, saying it could boost the automaker’s $52-billion market capitalization by as much as $38 billion.

Greenlight, which owns a 3.6 percent stake in GM, later nominated three directors for the company’s board: Leo Hindery, who served as CEO for five telecommunications and media companies, including AT&T Broadband and Liberty Media; Vinit Sethi, Greenlight’s director of research and William Thorndike, founder Housatonic Partners and the chairman of Consol Energy.

Greenlight hoped to replace three incumbent directors: Jane Mendillo, Michael Mullen and Carol Stephenson.

But Einhorn's pitch flopped with debt rating agencies and proxy advisers and he failed to rally other shareholders to his cause. Warren Buffett's Berkshire Hathaway Inc BRKa.N, which holds a 3.3 percent stake in GM, remained silent on the proposal.

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Einhorn added in Tuesday’s statement that GM should still consider Hindery and Thorndike for the board.

Greenlight is a multi-strategy hedge fund that has taken on other corporate giants such as Apple Inc AAPL.O, but whose last activist proxy contest was more than 10 years ago.

Jason Schloetzer, professor at Georgetown’s McDonough School of Business, said Greenlight’s loss is not a major blow to the roughly $10 billion hedge fund and time will tell if its stake earns the kind of returns Einhorn hopes to reap.

“While Greenlight would have liked to have increased their influence over GM’s financial management, it’s unfair to conclude from today’s vote that the fund will not be successful in its investment over the medium term,” Schloetzer said.