  Let n be greater than or equal to 3. We prove that the quaternion group of
order 8 is realised as a subgroup of the sphere braid group B\_n(S^2) if and
only if n is even. If n is divisible by 4 then the commutator subgroup of
B\_n(S^2) contains such a subgroup. Further, for all n greater than or equal to
3, B\_n(S^2) contains a subgroup isomorphic to the dicyclic group of order 4n.
