A family of permutation groups with exponentially many non-conjugated   regular elementary abelian subgroups
  Given a prime $p$, we construct a permutation group containing at least $p^{p-2}$ non-conjugated regular elementary abelian subgroups of order $p^3$. This gives the first example of a permutation group with exponentially many non-conjugated regular subgroups. 
Sergei Evdokimov, Mikhail Muzychuk, Ilia Ponomarenko
math.GR