California, United States — 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 US$100 million in annual revenue and fewer than 300 employees. Google’s size today — 24,400 employees and annual revenue of US$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.

To get back to its roots, Google concluded it needed to rearrange the hierarchy in place since technology veteran Eric Schmidt was brought in as CEO in 2001. It was an egalitarian arrangement, with Schmidt never having the final say on important matters. Page and Google’s other founder, Sergey Brin, always weighed in, too. In some cases, such as Google’s decision to move its search engine out of mainland China last year, the founders overruled Schmidt’s wishes.

In April, Schmidt will become executive chairman and relinquish the CEO duties to Page, now 37 and graying. While Schmidt travels the world meeting with business partners, government officials and potential takeover targets, Page says he will be making most of the big decisions as he tries to rekindle “the soul and passion of a startup.” Brin will concentrate on developing new products.

He’s worth US$15 billion, but Page remains something of a rebel who has always had a disdain for corporate protocol.

“Larry and Sergey both hate being organized. They don’t want to be locked into meetings,” says Ken Auletta, who got to know both of them while writing his book, “Googled: The End of the World as We Know It.”

While a free-wheeling attitude typically works well at small companies, it could cause problems in a company as large as Google, says Steve Booth, a business professor at the University of Chicago.

“The risk is that if you take away the process, that in some sense you go back to a kind of chaos,” Kaplan said.

Schmidt, 55, has no doubt Page is ready for the challenges ahead.

“Larry has been with me in every major decision in the past decade,” Schmidt said in an interview last week . “It’s not like he has been sitting around doing nothing.”

Although management by committee worked well enough to turn Google into an enormous success, it eventually slowed Google’s reaction to popular new ideas such as Facebook and Twitter. The bureaucracy has also caused Twitter and other startups to rebuff Google’s attempts to buy them. Some entrepreneurs who decided to sell to Google fled the company after a few months of frustration.

“Facebook is the most ominous threat to Google, but Facebook is just emblematic of the rising pace at which all of these (startups) are moving,” Wedbush Morgan analyst Lou Kerner says. “It’s Facebook today, it’s Groupon tomorrow, and it will be someone else after that.”

Google still hasn’t been able to develop an effective social networking tool to counter Facebook, a delay that could cost the company dearly as Facebook learns more about people’s ages, hometowns and passions. All that personal information is bound to help Facebook sell ads targeted at the audiences most likely to be interested in the products and services — a marketer’s dream.

“Facebook is attacking Google in its most important fortress, which is advertising revenue,” says Whit Andrews, an analyst at Gartner who has followed Google since 2000.

Google makes most of its money from ads that are triggered by search requests. For instance, someone searching for “flowers” would most likely see several links from florists. That’s the main way Google has built up a bank account that now has about US$35 billion in it. And it has left Google with a US$196 billion market value, with a single share in the company costing more than a basic iPad.

But it’s also saddled Google with the label of being a one-trick pony, even though it has been selling more ads with graphics, has branched out into a major player on mobile phones with its popular Android software and owns the Web’s top video site, YouTube.

Facebook also only does one trick well so far, but it could eventually command even more revenue than Google’s has.

By virtue of its design, Facebook engages its users with ads in a way Google cannot. It not only learns intimate details about users of its own website, but also on thousands of others as people press Facebook’s ubiquitous “Like” button to express their approval of everything from Levi’s jeans to a blog posting.

Facebook is expected to sell about US$4 billion in ads in 2011, its seventh year in business. By comparison, Google’s ad revenue totaled US$6 billion when it turned seven years old in 2005.

By then, Google had upstaged another Internet service that was once considered the Web’s coolest company — Yahoo Inc., which is now pinning its turnaround hopes on linking many of its services to Facebook and Twitter.