Suppose $\tau(n)$ is the number of divisors of a natural number $n$ and $s(G)$ is the number of subgroups of a finite group $G$. Is it always true, that $s(G) \geq \tau(|G|)$ for any finite group $G$?
This statement is true for finite abelian groups (follows from the classification of finite abelian groups and the fact, that $s(G \times H) \geq s(G)s(H)$). But is it true in general?
