The Iroquois (Oneida, Onondaga, Cayuga, Mohawk, Seneca) are a matriarchal society. In the Iroquois community, women were the keepers of culture. They were responsible for defining the political, social, spiritual and economic norms of the tribe. Iroquois society was matrilineal, meaning descent was traced through the mother rather than through the father. Also, when a couple marries, the man traditionally went to live with the wife's family. Although the leaders were men, it was the Clan Mothers who nominated and elected them, and could remove them from their position. The women made sure the male leadership fulfilled their responsibilities. Iroquois women enjoyed social equality and respect.
this type of governance served the tribes well until the British and French caused dissent by bribing males with whiskey, trinkets and false promises. I think a conservative female congress would keep everything in check.