Finite groups with generalized P-subnormal second maximal subgroups

A subgroup H of a group G is said to be K-P-subnormal in G [A. F. Vasilyev, T. I. Vasilyeva and V. N. Tyutyanov, On finite groups with almost all K-P-subnormal Sylow subgroups, in Algebra and Combinatorics: Abstracts of Reports of the International Conference on Algebra and Combinatorics on Occasion the 60th Year Anniversary of A. A. Makhnev (Ekaterinburg, 2013), pp. 19-20] if there exists a chain of subgroups H = H-0 <= H-1 <= . . . <= H-n = G such that either Hi-1 is normal in Hi or |H-i : Hi-1| is a prime, for i = 1, . . . , n. In this paper, we describe finite groups in which every second maximal subgroup is K-P-subnormal.