'Androcracy'/'gynocracy' are hyponyms of, and 'oligocracy'/'oligarchy' is a hypernym of, what term?
Solution 1:
I am unaware that there’s such a word in circulation. Not to worry, though. A feature of English is that you can always use productive prefixes and suffixes (including Greek and Latin ones) to modify an existing word, or, in effect, create a new one by analogy from an existing one, and be clearly understood.
The prefixes andro- and gyno- can be seen as subcategories of geno-, suggesting genocracy. Not quite there yet, since that means “rule by gender” and you’re looking for “rule by a single gender”, but we have mono- for that, so monogenocracy.
Note that you can reasonably argue that all three parts of the word are Greek. For some reason, mixed Latin and Greek roots get some peoples’ hair up.
What context this is useful for, I have no idea.