Gylany

[T]he two projected androcratic futures—a totalitarian future or no future at all—are not our only alternatives. There is the third alternative, the humanistic future to which the concept of gylany, both the balanced core and the logical requirement of our cultural evolution, provides the key.

Source: wiktionary

It seems particularly fitting to use terms of Greek derivation to describe how these two contrasting social models have affected our cultural evolution. For the conflict between gylany and androcracy as two very different ways of living on this earth—and the advancement of our evolution through gylanic influences—is dramatically illustrated if we take a fresh look at ancient Greece from the new perspective offered by cultural transformation theory.

Source: wiktionary

Old Europe and Anatolia, as well as Minoan Crete, were a gylany. A balanced, non-patriarchal and non-matriarchal social system is reflected by religion, mythologies, and folklore, by studies of the social structure of Old European and Minoan cultures, and is supported by the continuity of the elements of a matrilinear system in ancient Greece, Etruria, Rome, the Basque, and other countries of Europe.

Source: wiktionary

In a gylany, the sexes are "linked" rather than hierarchically "ranked" which is typical of patriarchal societies. The existence of gylanies or societies with a balanced authority among men and women has been evidenced by ethnology and anthropology. Gylany must not be confused with matriarchy which never existed and which has the value of a myth like the one about the Amazons[…]. Civilization in Old Europe is among the examples of an early gylany in mankind's cultural history.

Source: wiktionary