matriarchy

Concise Oxford English Dictionary © 2008 Oxford University Press:
matriarchy /ˈmeɪtrɪɑːki/

▶noun (pl. matriarchies)

• 1 a system of society or government ruled by women.

• 2 a form of social organization in which descent and relationship are reckoned through the female line.

– derivatives
matriarchal adjective.