What is the term for an oligocratic/oligarchic political system—one in which power is held by a subset of the overall population—where the power allocation is based on one's sex?
A society run by men is an 'androcracy', and one run by women a 'gynocracy'. I am looking for the hypernym of these terms, which would simultaneously be a hyponym of 'oligocracy'. If one does not yet exist, what might we reasonably coin based on whatever the Greek term for 'sex' is, plus -cracy?
(As an extra linguistics question, would 'the mesonym between x and y' be correct to use for what I'm looking for here, rather that 'the hypernym of x and the hyponym of y'?)