Groups with finitely many isomorphism classes of non-modular subgroups

Groups in which the non-moduar subgroups fall into finitely many isomorphism classes are considered, and it is proved that a (generalized) soluble group with this property either has modular subgroup lattice or is a minimax group. The corresponding result for (generalized) soluble groups with finitely many isomorphism classes of non-permutable subgroups is also obtained.