Are Conjugacy classes subgroups?

The subgroups can thus be divided into conjugacy classes, with two subgroups belonging to the same class if and only if they are conjugate. ... For example, an abelian group may have two different subgroups which are isomorphic, but they are never conjugate. Conjugacy as group action. read more

The subgroups can thus be divided into conjugacy classes, with two subgroups belonging to the same class if and only if they are conjugate. Conjugate subgroups are isomorphic, but isomorphic subgroups need not be conjugate. read more

The elements of the poset correspond to the conjugacy classes of subgroups. Two lattice elements a and b are joined by an edge if either some subgroup of the conjugacy class a is a maximal subgroup of some subgroup of conjugacy class b or vice-versa. read more