As contrasted to ‘patriarchy':
Kyriarchy – a neologism coined by Elisabeth Schussler Fiorenza and derived from the Greek words for “lord” or “master” (kyrios) and “to rule or dominate” (archein) which seeks to redefine the analytic category of patriarchy in terms of multiplicative intersecting structures of domination…Kyriarchy is best theorized as a complex pyramidal system of intersecting multiplicative social structures of superordination and subordination, of ruling and oppression.
Patriarchy – Literally means the rule of the father and is generally understood within feminist discourses in a dualistic sense as asserting the domination of all men over all women in equal terms. The theoretical adequacy of patriarchy has been challenged because, for instance, black men do not have control over white wo/men and some women (slave/mistresses) have power over subaltern women and men (slaves).
– Glossary, Wisdom Ways, Orbis Books New York 2001
Put like that, it seems pretty clear which term is the most useful for making sense of reality. Many thanks to Sudy at A Woman’s Ecdysis for introducing her readers to the term!