Why does the GroupNames.org table of transitive groups omit $S_6$ and $S_7$?

Question

Obviously $S_n$s are all transitive. But GroupNames.org's "Transitive groups of degree up to 31" table seems not to include $S_6$, $S_7$. Tell me why.

(And I also don't figure out reason why $C_{23}\rtimes C_{22}$ is not in the table..?)

Sorry if I make elementary mistakes.