Finite groups that are products of two normal supersoluble subgroups

Let $\mathfrak{P1}$ be the class of all finite groups that are products of two normal supersoluble subgroups. Let $\mathfrak P$ be the class of all nonsupersoluble $\mathfrak{P1}$-groups $G$ such that all proper $\mathfrak{P1}$-subgroups of $G$ and nontrivial factor groups of $G$ are supersoluble. We classify the $\mathfrak P$-groups.