Once a year, a small group of executives who control trillions of dollars in American companies meet for lunch in Manhattan. Among the things they discuss: pushing for greater say in how companies are run.

It is an elite gathering, but you will not see a single man in a suit in the room. The event, called the Women in Governance lunch, underscores a rare corner in finance where women dominate.

Women hold the top positions in corporate governance at many of the biggest mutual funds and pension funds — deciding which way to vote on the directors of a company board. They make decisions on behalf of teachers, government workers, doctors and most people in the United States who have a 401(k). The corporate governance heads at seven of the 10 largest institutional investors in stocks are now women, according to data compiled by The New York Times. Those investors oversee $14 trillion in assets.

Corporate governance is playing a growing role within the broader ecosystem of corporate America. Each spring, publicly traded companies hold shareholder meetings and outline business strategy for the coming year. Shareholders like BlackRock, T. Rowe Price and State Street vote on corporate strategy and issues including company board appointments and compensation.