Suppose I was asked if [itex] G \cong H \times G/H [/itex]. At first I considered a familiar group, [itex]G = S_3 [/itex] with its subgroup [itex]H = A_3 [/itex]. I know that the quotient group is the cosets of [itex]H[/itex], but then I realized that I have no idea how to interpret a Cartesian product of any type of set with elements that aren't just numbers. An ordered pair of permutations doesn't make sense (this is not a homework question). I'd be grateful for some clarity.