  Let $G$ be a finite group acting on a ring $R$ and $H$ a subgroup of $G$. In
this paper we compare some homological dimensions over the skew group rings
$RG$ and $RH$. Moreover, under the assumption that $RG$ is a separable
extension over $RH$, we show that the skew group rings $RG$ and $RH$ share some
properties such as being $n$-Gorenstein, $n$-perfect, $n$-coherent, $(n,d)$,
Ding-Chen or IF-rings.
