The club is not exactly an exercise in democracy. To become a member, an applicant must be nominated by one of 1,200 existing members. (The first 100 were handpicked by the Birches.) Applicants are reviewed by a committee, details of which the Birches declined to discuss. But the couple did stress that the club strives for diversity, at least in terms of profession (“You can’t just have tech people because those conversations get boring,” Ms. Birch said) and gender (too many bros does not a party make).

There is also an annual fee of $2,400, which Ken Fulk, the club’s creative director, said “is about what you’d pay for a nice gym in the city.” That’s comparable to the fee at other private clubs like the Soho House in New York, though it should be noted that the Battery also charges an additional $70 a month to use the gym and spa. (The Battery also offers “scholarships” for members whose fortunes are not tied to I.P.O.’s.)

Once in, there are rules or “customs,” as the Battery likes to call them. Members receive a book detailing protocols such as, “members should check their coats and egos at the door,” and “talking business is welcome; pitching business is not.” For its always-wired members, the toughest rule may be its ban on posting anything club-related on Instagram, Facebook and other social networks. Talking or texting on cellphones is also discouraged after 6 p.m.

“We just want members to feel like they can come, relax, and not feel like they’re going to end up posted on some social media thing,” Mr. Birch said. (Photography is also banned, though the Birches agreed to pose inside the club for this article.)

Arbiters of the city’s night life have not exactly embraced the Battery. Some say it is the latest example of how San Francisco is increasingly geared for the rich.

“Another lavish private club you can’t afford,” said the blog Sfist. Others have been underwhelmed by the crowd, saying that it is too network-y.