In this setting, the family unit is based around a clan system. An individual's wealth and status is related to the clan they are born in, and its ancestry is based on matrilineal lines. Due to certain environmental factors on the continent, travel between regional areas can be somewhat difficult and expensive. Therefore, most breeding takes place between clans in relative proximity of each other.
Marriage does not exist in the form we would recognize. Women remain in the clan they were born into, while men are the ones who leave the home to join other families. Men don't marry an individual, instead they marry into an entire clan. This leads to many offspring coming from the same group of fathers. A cultural belief system has developed in which boys are considered "sons of society" and raised in bulk while girls are "daughters of their mothers" and raised specifically by their mother.
How can this society avoid genetic inbreeding under these circumstances?