On intersections of solvable Hall subgroups in finite nonsolvable groups

The author continues the investigation of intersections of Hall subgroups in finite groups. Previously, the author proved that in the case when a Hall subgroup is Sylow there are three subgroups conjugate to it such that their intersection coincides with the maximal normal primary subgroup. A similar assertion holds for Hall subgroups in solvable groups. The aim of this paper is to construct examples of a (nonsolvable) group in which the intersection of any four subgroups conjugate to some Hall subgroup is nontrivial.