Gynecocracy
The opposite of androcracy is gynecocracy, sometimes referred to as gynocracy, or rule by women. It is related to but not synonymous with matriarchy. Evidence indicating historical gynecocracies survives mostly in mythology and in some archaeological records, although it is disputed by some authors, like Cynthia Eller in her book The Myth of Matriarchal Prehistory.
Through scientific excavations of ancient sites, archaeologists have recently obtained a great deal of Neolithic data for re-evaluation and reconstruction of our past, indicating neither androcracy nor gynecocracy, but rather equalitarianism, i.e., women as priestesses and heads of clans seem to have played leading roles in all aspects of life, descent appears to have been traced through the mother, therefore men were subordinate.
Read more about this topic: Androcracy