# Estimating Number Of normal subgroups of a p-Group

Does someone have an idea about a possible way to count the number of normal subgroup that a group of order $p ^n$ has ($n \in \mathbb{N}$ )? Is there anyway we can count the maximal subgroups it has (i.e.- the groups of order $p^{n-1}$ ? ) ?

Counting maximal subgroups is equivalent to counting p-cycles in the elementary abelian group $P/\phi(P)$. –  peoplepower Oct 1 '12 at 23:38