  Let $W$ be a finite group and $T$ be an abelian group. Consider an extension
$0 \ra T \ra N \ra W \ra 0$. For a smooth projective curve $X$, we give a
precise description of the fiber of the quotient by $T$ map $q_T: \cM_X(N) \ra
\cM_X(W)$ as a torsor over an abelian variety. We also prove a result on
Mumford groups.
