Subgroups of $\operatorname{SL}_n$ over a semilocal ring

In the present paper we prove that if $R$ is a commutative semi-local ring all of whose residue fields contain at least $3n+2$ elements, then for every subgroup $H$ of the special linear group $\operatorname{SL}(n,R)$, $n\ge 3$, containing the diagonal subgroup $\operatorname{SD}(n,R)$ there exists a unique $D$-net $\sigma$ of ideals $R$ such that $\mathrm{G}(\sigma)\le H\le N_{\mathrm{G}}(\sigma)$. In the works by Z. I. Borewicz and the author similar results were established for $\operatorname{GL}_n$ over semi-local rings and for $\operatorname{SL}_n$ over fields. Later I. Hamdan obtained similar description for a very special case of uniserial rings.