  Let $\mathcal G\simeq H\rtimes\Gamma$ be the semidirect product of a finite
group $H$ and $\Gamma\simeq\mathbb Z_p$. Let $F/\mathbb Q_p$ be a finite
extension with ring of integers $\mathcal O_F$. Then the total ring of
quotients $\mathcal Q^F(\mathcal G)$ of the completed group ring $\mathcal
O_{F}[[\mathcal G]]$ is a semisimple ring. We determine its Wedderburn
decomposition by relating it to the Wedderburn decomposition of the group ring
$F[H]$.
