| 1 | G ≤ Sym(12) | 12-trans., on cosets of S11 (2nd max.) |
| 2 | G ≤ Sym(66) | rank 3, on cosets of S10 × 2 (3rd max.) |
| 3 | G ≤ Sym(220) | rank 4, on cosets of S9 × S3 (4th max.) |
| 4 | G ≤ Sym(462) | rank 4, on cosets of (S6 × S6):2 (5th max.) |
| 5 | G ≤ Sym(495) | rank 5, on cosets of S8 × S4 (6th max.) |
| 6 | G ≤ Sym(792) | rank 6, on cosets of S7 × S5 (7th max.) |
| 7 | G ≤ Sym(5040) | rank 8, on cosets of M12 < A12 |
| 8 | G ≤ Sym(5775) | rank 9, on cosets of S4 ≀ S3 (8th max.) |
| 9 | G ≤ Sym(10395) | rank 11, on cosets of 26:S6 (9th max.) |
| 10 | G ≤ Sym(15400) | rank 12, on cosets of S4 ≀ S3 (10th max.) |
File created automatically by GAP on 22-Apr-2022.