I am interested in families of finite groups arising from direct products of other groups. For instance, abelian groups are a simple example of such families (direct products of cyclic groups), but there are more. The family of hamiltonian groups is another such family; a hamiltonian group is a group where all the subgroups are normal, and it can be expressed as the direct product of the quaternion group of order 8, an abelian group of odd order and a group formed only by involutions. Coxeter groups are other examples; they are represented as direct products of irreducible Coxeter groups.


Could you point out to any other such families??


Thanks in advance, and regards,
Guillermo



Families of finite groups arising from direct products...
A finite group is nilpotent iff it is a direct product of $p$-groups.


