J an 2 00 6 On the Orbit Decomposition of Finite Quandles

We study the structure of finite quandles in terms of subquandles. Every finite quandle Q decomposes as a union of disjoint Q-complemented subquandles which coincide with the orbits of Q. Conversely, the structure of a quandle with a given orbit decomposition is determined by rack actions satisfying a compatibility condition. We include Maple code for finding orbit decompositions and quandle structures on disjoint unions of quandles.