Sorry if others have posted this already - I haven't read the thread yet.
Patriarchy is simply male dominance or male rule.
When feminists say 'the patriarchy' it is a bit of a slang personification of an abstraction - similar to when civil rights activists refer to 'The Man'.
There isn't really a singular 'man' or conspiratorial group of patriarchs organising specifically to perpetuate male dominance, although there are some groups that look lot like it - for instance the Catholic patriarchy who have historically had HUGE global dominance above monarchs and who specifically deny the ordination of women, or male pornographers who dream up ways to quarry female bodies and souls to near destruction as a way to glorify male sexual dominance.
Because male dominance is so complete and universal: Who leads and who obeys in every culture? - it not only organises the way humans relate to one-another overtly or through 'tradition', it has its stamp upon the very language we speak and words we write, the way we are raised to view the world, how we view others and our selves. It has its stamp on the knowledge that is passed to us and the knowledge that is suppressed, what is considered the norm and what is considered 'other'. It is a 'total dominance' of one sexual class by the other.
So if (to reference something upthread) there is a matriarchy (female dominated/organised group of people) within the wider patriarchy, the language, thought,etc will still reference that wider patriarchy, so it will manifest very differently to a patriarchy and could never be a 'total dominance' by women.