For every chair occupied by a woman in the corporate C-suite, six are filled by a man.

In the federal government, it’s 1 out of every 3.

Women are gradually advancing to the highest levels of government, where they now represent 33.7 percent of the leaders known as senior executives. These are the mostly career managers who carry out the mandate of the White House, occupying key roles just below top presidential appointees. In the civilian world, they’re the generals and admirals who run their agencies day-to-day.

Women and men have not reached parity in the top ranks of government. But among the 7,187 career senior executives, they’ve reached pay parity, with women getting a slight edge. Their $175,451 average salary is $479 more than men’s.

Women have climbed further than their male counterparts at private companies, where just 16 percent of executives are women, according to an analysis by McKinsey & Company, working with the Partnership for Public Service.

The Government Accountability Office, a little-known agency that acts as the government’s fiscal watchdog, has quietly cultivated a culture that has helped women thrive. The result? Women make up 41 percent of the senior executives there, substantially above the government-wide average.

The GAO has what’s best described as an unglamorous mission: It audits government programs for Congress to ensure that taxpayers get the most efficient and accountable spending for their money.

The audits released this month include titles such as “Agencies Have Sound Procedures for Managing Exchanges but Could Improve Inventory Monitoring” (on nuclear material) and “Guidance Needed for Completing Required Impact Assessments Prior to Presidential Drawdowns” (on security assistance).

Arcane as the work is, it gets results: Federal agencies act on about 80 percent of the GAO’s recommendations to improve their operations, even if some guidance takes years to be implemented.

Yet the GAO is not just a good place to work (it consistently ranks near the top among midsize agencies in the Best Places to Work in the Federal Government annual rankings) but a good place to work for women. Of the agency’s 121 senior executives, 50 are women, including the general counsel and chief operating officer.

“With the wide variety of work we’re doing, you want to have a representative workforce,” Eugene Dodaro, the comptroller general of the United States and GAO head, said in an interview.

Government agencies have long prided themselves on helping their employees balance their work and personal lives. The GAO’s approach is more serious than most: day care on site at the Washington headquarters, a student loan repayment program, a generous telework policy — 65 percent of the staff worked from home one day or more per pay period last year — and a flexible relocation policy.

When she was hired 26 years ago as an entry-level analyst right out of graduate school, Orice Williams Brown told herself she would do this for a few years until the financial markets, still reeling from a crash, recovered.

Her first assignment was to investigate why the Internal Revenue Service was not using interest on municipal bonds that local governments had returned to the federal government. “I was totally hooked,” she recalled.

She was promoted to senior executive in 2005, in charge of the team that audits financial markets and community investment. Five years ago, she was made a managing director.

“The work is extremely appealing,” Williams Brown, 50, said. “It’s a family-friendly culture. I’ve seen people advance regardless of where they are in their personal life. I’ve seen people promoted who are out on maternity leave.”

She said that by having employees work in teams with experts from different disciplines, the GAO puts a premium on collaborative skills and coming to collective decisions. “That’s one of the things women are really socialized to do.”

For Susan Poling, the GAO’s stable leadership is a big factor in why she and other women thrive. The agency is not run by a political appointee whose face changes every four years, but by a nonpartisan civil servant who serves a 15-year term.

Like many lawyers, Poling found that government gives women opportunities to advance without working the 70-and 80-hour weeks that are essential to making partner at corporate firms.

“One of the things I bring is that I’ve been a working mother, and I have other men and women on my staff who are working parents,” she said.

When she was hired to the GAO in 1990 from the Department of Education, she worked part time so she could spend more time with her young son. “But they didn’t shunt me over and not give me great things to do,” she said.

Today, as a full-time senior executive, Poling supervises 156 lawyers.

And at 68, she has no plans to retire anytime soon. “I’m still enjoying myself.”