  A nonabelian finite flavor group $G \subset SO(3)$ can have double covering
$G^{'} \subset SU(2)$ such that $G \not\subset G^{'}$. This situation is not
contradictory, but quite natural, and we give explicit examples such as $G=D_n,
G^{'}=Q_{2n}$ and $G=T, G^{'}=T^{'}$. This observation can be crucial in
particle theory model building.
