  Let $S$ be a complete intersection of a smooth quadric 3-fold $Q$ and a
hypersurface of degree $d$ in ${\mathbb P}^4$. In this paper we analyze GIT
stability of $S$ with respect to the natural $G=SO(5, {\mathbb C})$-action. We
prove that if $d\ge 4$ and $S$ has at worst semi-log canonical singularities
then $S$ is $G$-stable. Also, we prove that if $d\ge 3$ and $S$ has at worst
semi-log canonical singularities then $S$ is $G$-semistable.
