The number of conjugacy classes of nonnormal subgroups of finite p-groups (III)

Abstract

Assume [Formula: see text] is a positive integer and [Formula: see text] is an odd prime. Let [Formula: see text] be the number of conjugacy classes of nonnormal subgroups of a finite group [Formula: see text] and [Formula: see text] is a finite [Formula: see text]-group[Formula: see text]. The set [Formula: see text] has been determined for [Formula: see text]. In this paper, the set [Formula: see text] is determined, and it is discovered that there are three gaps in the values that [Formula: see text] can take in the case of finite [Formula: see text]-groups.