Finite groups with $S$-conditionally permutable Schmidt subgroups

A subgroup $H$ in a finite group $G$ is $S$-conditionally permutable if for every $p\in \pi (G)$ there exists a Sylow $p$-subgroup $P$ in $G$ such that $HP=PH$. We study the structure of a finite group $G$ whose all Schmidt subgroups are $S$-conditionally permutable.