Solvability of $S_3\times S_3$ I know that the direct product of two solvable groups are solvable. The group $S_3$ is solvable, so $S_3\times S_3$ is solvable. But how am I going to establish the subnormal series of $S_3\times S_3$?or is there any simpler way to show its solvability?
Thanks.

$$\langle\omega\times\omega\rangle \trianglelefteq \langle\omega\rangle\times A_3 \trianglelefteq A_3\times A_3 \trianglelefteq A_3\times S_3 \trianglelefteq S_3\times S_3$$
