You searched for: “gynandrarchy
gynandrarchy (s) (noun), gynandrarchies (pl)
1. A social organization among insects differing from gynarchy: Gynandrarchy interested Mary and she found out that the male insect takes part in establishing the colony.
2. Rule or government by a man and a woman, or by both men and women: Doug thought that a form of gynandrarchy would provide a way of having complete equality of both men and women when making important decisions for the benefit of all citizens.