A Schmidt group is a finite non-nilpotent group such that every proper subgroup is nilpotent.
In this paper, we prove that if every Schmidt subgroup of a finite group πΊ is subnormal or modular, then
G
/
F
β’
(
G
)
G/F(G)
is cyclic.
Moreover, for a given prime π, we describe the structure of finite groups with subnormal or modular Schmidt subgroups of order divisible by π.