Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20261366 | C2 | semidirect |
| 3. #20261098 | C2 | semidirect |
| 4. #20261093 | C2 | semidirect |
| 5. #20261088 | C2 | semidirect |
| 6. #20261080 | C2 | semidirect |
| 7. #20260740 | C2 | semidirect |
| 8. #20260734 | C2 | semidirect |
| 9. #20260732 | C2 | semidirect |
| 10. #20260690 | C2 | semidirect |
| 11. C2×#102×C97 | C2 | semidirect |
| 15. #15690809 | C22 | semidirect |
| 18. #15690801 | C22 | semidirect |
| 26. #15690735 | C22 | semidirect |
| 27. #15690735 | C22 | semidirect |
| 28. #15690733 | C22 | semidirect |
| 29. #15690732 | C22 | semidirect |
| 30. #15690732 | C22 | semidirect |
| 33. #15690730 | C22 | semidirect |
| 34. #15690720 | C22 | semidirect |
| 35. C8×Dic97 | C22 | semidirect |
| 136. C97 | #3136 | semidirect |
| 146. C2×#102 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261366 | 2 |
| #20261302 | 2 |
| #20261098 | 2 |
| #20261093 | 2 |
| #20261088 | 2 |
| #20261080 | 2 |
| #20260740 | 2 |
| #20260734 | 2 |
| #20260732 | 2 |
| #20260690 | 2 |
| C2×#102×C97 | 2 |
| #3136 | 97 |