In 1898 George Miller delineated the structure of a Hamiltonian group in terms of its order and that of its subgroups. For instance, he shows "a Hamilton group of order 2a has quaternion groups as subgroups". In 2005 Horvat et al used this structure to count the number of Hamiltonian groups of any order where o is an odd integer. When then there are no Hamiltonian groups of order n, otherwise there are the same number as there are Abelian groups of order o.
In 1898 George Miller delineated the structure of a Hamiltonian group in terms of its order and that .of its subgroups. For instance, he shows "a Hamilton group of order 2a has quaternion groups as subgroups". In 2005 Horvat et al used this structure to count the number of Hamiltonian groups of any order where o is an odd integer When then there are no Hamiltonian groups of order n, otherwise there are the same number as there are Abelian groups of order o.