Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
596 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#15690834 | C2 | semidirect |
| 2. C2×#15690829 | C2 | semidirect |
| 3. C2×D8×D97 | C2 | semidirect |
| 4. #20261298 | C2 | semidirect |
| 5. #20261123 | C2 | semidirect |
| 6. #20261122 | C2 | semidirect |
| 7. #20261119 | C2 | semidirect |
| 8. #20261118 | C2 | semidirect |
| 9. #20261110 | C2 | semidirect |
| 10. #20260689 | C2 | semidirect |
| 11. #493×C97 | C2 | semidirect |
| 16. C2×Dic388 | C22 | semidirect |
| 17. C2×#13095500 | C22 | semidirect |
| 18. C2×#13095499 | C22 | semidirect |
| 19. C2×#13095499 | C22 | semidirect |
| 22. C2×#13095496 | C22 | semidirect |
| 26. #15690806 | C22 | semidirect |
| 27. #15690798 | C22 | semidirect |
| 28. #15690797 | C22 | semidirect |
| 32. #15690721 | C22 | semidirect |
| 33. #15690720 | C22 | semidirect |
| 34. C8×Dic97 | C22 | semidirect |
| 36. C2×D8×C97 | C22 | semidirect |
| 37. C2×D8×C97 | C22 | semidirect |
| 38. #127×C97 | C22 | semidirect |
| 39. C4×C8×C97 | C22 | semidirect |
| 59. #13095494 | D4 | semidirect |
| 62. C8×D97 | D4 | semidirect |
| 130. C97 | #3155 | semidirect |
| 140. #493 | D97 | semidirect |
| 155. C2×D8 | C2×D97 | semidirect |
| 156. C2×D8 | C2×D97 | semidirect |
| 160. #127 | C2×D97 | semidirect |
| 169. C4×C8 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690834 | 2 |
| C2×#15690829 | 2 |
| C2×D8×D97 | 2 |
| #20261298 | 2 |
| #20261123 | 2 |
| #20261122 | 2 |
| #20261119 | 2 |
| #20261118 | 2 |
| #20261110 | 2 |
| #20260689 | 2 |
| #493×C97 | 2 |
| #3155 | 97 |