San Francisco ? Google is richer than ever, but it’s not as cool as it once was.

Facebook boasts 500 million members who share 30 billion links, notes and photos each month — data that Google’s search engine can’t completely index. It’s so influential that 26-year-old founder Mark Zuckerberg was just named Time’s person of the year, and a movie about the company’s early days is a contender for best picture at the Oscars.

Twitter, Groupon and Foursquare, all hard-charging and potentially game-changing services, are additional thorns in Google’s side, raising worries that the online search leader may be losing the competitive edge that turned it into the Internet’s most powerful company.

Making Google hip and nimble again will be the priority as Larry Page, one of the two Stanford University students who founded the company in a garage in 1998, prepares to reclaim the CEO job in a shake-up that surprised Silicon Valley.

He last held it a decade ago, when Google Inc. had less than $100 million in annual revenue and fewer than 300 employees. Google’s size today — 24,400 employees and annual revenue of $29 billion — has slowed its decision-making and innovation in the past few years.

About 200 of Facebook’s 2,000 employees defected from Google, and the migration appears to be about more than just the allure of getting stock options in a hot company before it goes public. Some engineers seem to be drawn by the work at a smaller company, which offers an opportunity to reshape culture with less corporate bureaucracy and more creative freedom.

“Facebook has become the cool kid on the block, and now Google wants to prove it can still be cool, too,” says Danny Sullivan, who follows both companies closely as editor-in-chief of Search Engine Land.

It’s not an impossible feat, says Michael Cusumano, an MIT professor of management. As an example, he cites IBM, which seemed on its way to becoming a tech dinosaur in the early 1990s before Louis Gerstner arrived as CEO and streamlined the company.