中文摘要：

设G是有限群，π（G）表示G的阶的素因子集合，μ（G）表示G的非次正规子群的共轭类类数。本文证明了满足条件μ（G）≤2｜π（G）｜的有限群G可解，并完全刻画非次正规子群共轭类类数不大于群的阶的素因子个数的有限群，即满足不等式μ（G）≤｜π（G）｜的有限群G的结构。

英文摘要：

Let G be a finite group, π（G） be the set of prime factors dividing ｜G｜ and μ（G） denote the number of conjugacy classes of all non-subnormal subgroups of G. In this paper, it is shown that all finite groups G with μ （G）2 ｜π（G） ｜ are solvable and that the structure of finite groups having at most ｜π（G）｜ conjugacy classes of non-subnormal subgroups are completely characterized.