Symmetric Group on 3 Letters/Normal Subgroups/Cayley table of Quotient Group

Normal Subgroups of the Symmetric Group on 3 Letters
Let $S_3$ denote the Symmetric Group on 3 Letters, whose Cayley table is given as:

Let $H$ denote the normal subgroup $\set {e, \tuple {123}, \tuple {132} }$.

Let $K$ denote the coset of $H$ in $S_3$.

The Cayley table of the quotient of $S_3$ by $H$ is given as:


 * $\begin {array} {c|cc} S_3 / H & H & K \\ \hline H & H & K \\ K & K & H \end {array}$