I want to construct some Sylow $3$-subgroup of $S_{11}$.This subgroup has $3^4$ elements. I know any Sylow $3$-subgroup is isomorphic to $(\mathbb{Z}/3\mathbb{Z})^3\rtimes P$ where $P$ is a Sylow $3$-subgroup of $S_3$.
But when I write $$H=\langle(123)\rangle\oplus\langle(456)\rangle\oplus\langle(789)\rangle\oplus\mathord{?}$$ why can't we find fourth direct summand? Could anyone explain this fact? Thanks.