‘Structure of groups’ discusses the basic concepts of group theory. Isomorphism occurs when two technically distinct groups share the same abstract structure and order. Groups may also contain smaller subgroups — the orders of subgroups are divisions of the order of the whole group. Two symmetries of some objects may be essentially the same, but applied at different locations — a phenomenon known as conjugacy. A conjugacy class is a set of all elements conjugate to a given element. Quotient groups are a special kind of partition of a group, which can give rise to homomorphisms (which is related to isomorphisms), and normal groups.