Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#13095496 | C2 | semidirect |
| 2. C2×#15690817 | C2 | semidirect |
| 3. #20261299 | C2 | semidirect |
| 4. #20260986 | C2 | semidirect |
| 5. #20260969 | C2 | semidirect |
| 6. #20260771 | C2 | semidirect |
| 7. #20260740 | C2 | semidirect |
| 8. #20260739 | C2 | semidirect |
| 9. #535×C97 | C2 | semidirect |
| 16. C2×#13095495 | C22 | semidirect |
| 18. C22×#11715895 | C22 | semidirect |
| 21. #15690784 | C22 | semidirect |
| 24. #15690743 | C22 | semidirect |
| 25. #15690741 | C22 | semidirect |
| 26. #15690731 | C22 | semidirect |
| 27. #15690730 | C22 | semidirect |
| 32. #121×C97 | C22 | semidirect |
| 46. C2×#11715895 | D4 | semidirect |
| 126. C97 | #3058 | semidirect |
| 130. #535 | D97 | semidirect |
| 152. #121 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095496 | 2 |
| C2×#15690817 | 2 |
| #20261299 | 2 |
| #20260986 | 2 |
| #20260969 | 2 |
| #20260771 | 2 |
| #20260740 | 2 |
| #20260739 | 2 |
| #535×C97 | 2 |
| #3058 | 97 |