A group formed by the cosets of a normal subgroup. Let G/H denote the set of cosets of a subgroup H of a group G. The group operation on G induces a well-defined group operation on G/H given by (g₁H)(g₂H) = (g₁g₂)H if and only if H is a normal subgroup of G, By Lagrange’s theorem, if G is finite then G/H has order |G|/|H|.