It is matriarchal, as when the first Awoken were “reborn” (awakened, if you will), the overwhelming majority were women. Thus, they organized their society as a matriarchy to protect the men they had, and it stuck. Men do still operate in military capacities, though they are a minority. Take Paladin Hallam Fen, promotes from Commander after proving himself at Pallas. He has operated as a ranking officer for quite some time, evidently. Just because it’s matriarchal doesn’t mean it’s not equal opportunity! 😉