| 1 | G ≤ Sym(12) | 12-trans., on cosets of S11 (2nd max.) |
| 2 | G ≤ Sym(66) | rank 3, on cosets of S10 (3rd max.) |
| 3 | G ≤ Sym(220) | rank 4, on cosets of (A9 × 3):2 (4th max.) |
| 4 | G ≤ Sym(462) | rank 4, on cosets of (A6 × A6):22 (5th max.) |
| 5 | G ≤ Sym(495) | rank 5, on cosets of (A8 × A4):2 (6th max.) |
| 6 | G ≤ Sym(792) | rank 6, on cosets of (A7 × A5):2 (7th max.) |
| 7 | G ≤ Sym(5040) | rank 8, on cosets of M12 < A12 |
| 8 | G ≤ Sym(5775) | rank 9, on cosets of 26:33:S4 (8th max.) |
| 9 | G ≤ Sym(10395) | rank 11, on cosets of 25:S6 (9th max.) |
| 10 | G ≤ Sym(15400) | rank 12, on cosets of 34:23.S4 (10th max.) |
File created automatically by GAP on 22-Jun-2011.