Finite subquandles of sphere

In this work finite subquandles of sphere are classified by using classification of subgroups of orthogonal group O(3) . For any subquandle Q of sphere there is a subgroup GQ of O(3) associated with Q. It is shown that if Q is a finite (infinite) subquandle, then GQ is a finite (infinite) subgroup. Finite subquandles of sphere are obtained from actions of finite subgroups of SO(3) on sphere. It is proved that the finite subquandles Q_1 and Q_2 of sphere whose all elements are not on the same great circle are isomorphic if and only if the subgroups G_Q1 and G_Q2 of O(3) are isomorphic by which finite subquandles of sphere are classified.