Religious orders never really developed in Orthodox Christianity the way it happened in the West--a monk is a monk is a monk. You don't have Benedictines, Franciscans, Carmelites, Dominicans, or any other distinct monastic rites in Eastern Christianity. While you did have entire armies who waged war against invading Muslim peoples in the name of defending their Christian lands (including even some bishops who took up weapons and died on the battlefield that later got recognition as saints), this wasn't part of anything like the Templars or the Hospitaliers. They were just soldiers who fought in the name of land and faith.