On the problem of intersections of the maximal $\theta$-subgroups of finite groups

Let $\mathfrak{F}$ be a nonempty formation, $\pi$ — some set of prime numbers. The theorems reflecting the general regularities on intersections of maximal subgroups of a finite group mutually simple with numbers from $\pi$ indexes including statements on the intersections $\Phi_{\pi,\overline{\widetilde{F}_{\Phi_\pi}(G)}}(G)$ and $\Delta^{\mathfrak{F}}_{\pi,\overline{\widetilde{F}_{\Delta^{\mathfrak{F}}_\pi}(G)}}(G)$ are received.