A group of order 56 has a normal Sylow subgroup
= A group of order 56 has a normal Sylow subgroup
The <Sylow theorems> give either one or eight <Sylow subgroups> of order seven. In the first case that <subgroup> is normal. In the second, their six nonidentity elements are pairwise disjoint, accounting for 48 elements. Only eight elements remain, including the identity, and every <Sylow subgroup> of order eight lies entirely among them. Thus there is exactly one, and it is a <normal subgroup>.