genus, subordinate official, belong, affiliated
屬 centers on connection and classification: belonging to a group, being affiliated, or serving as a subordinate. The genus sense extends this to a formal category that things belong to.
屬 is the traditional form of 属. It combines 㞑 (a tail-like component suggesting connection) with 蜀, which likely contributes the sound. The idea of a tail attached to a body fits the core meaning of belonging or affiliation.
The outer 㞑 looks like a tail attached to the inner 蜀. Picture a tail that belongs to a creature, symbolizing how things are affiliated or belong to a group.
For ゾク, imagine a zookeeper organizing animals by genus: zook -> ゾク, and each animal belongs to its proper category.