Let <i>G</I> be a group and <I>H</i> a subgroup of <I>G</I>.  Let <I>S</I> be the group of all permutations of the left cosets of <I>H</I> in <I>G</i>.
  Then there is a homomorphism from <I>G</I> into <I>S</I> whose kernel lies in <I>H</I> and contains every normal subgroup of <I>G</I> that is contained in <I>H</I>.