You searched for: “gynocracy
gynocracy, gynecocracy, gyneocracy (s) (noun); gynocracies; gynecocracies; gyneocracies (pl)
A government by a woman or women: A form of gynocracy is a country in which women are legally capable of the supreme command, for example the former Queen in Great Britain.

A gynocracy is sometimes used in a depreciative sense as "petticoat rule".