Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20261531 | C2 | semidirect |
| 2. C2×#15690829 | C2 | semidirect |
| 3. #131×D97 | C2 | semidirect |
| 4. #20261011 | C2 | semidirect |
| 5. #20261010 | C2 | semidirect |
| 6. #20261002 | C2 | semidirect |
| 7. #20260997 | C2 | semidirect |
| 8. #20260996 | C2 | semidirect |
| 9. #108×D97 | C2 | semidirect |
| 10. #20260716 | C2 | semidirect |
| 11. #472×C97 | C2 | semidirect |
| 25. C2×Dic388 | C22 | semidirect |
| 26. C2×#13095499 | C22 | semidirect |
| 37. #15690746 | C22 | semidirect |
| 38. #15690745 | C22 | semidirect |
| 39. #15690728 | C22 | semidirect |
| 40. #15690728 | C22 | semidirect |
| 41. #15690727 | C22 | semidirect |
| 43. C2×D8×C97 | C22 | semidirect |
| 45. #108×C97 | C22 | semidirect |
| 46. #100×C97 | C22 | semidirect |
| 167. C97 | #3067 | semidirect |
| 174. #472 | D97 | semidirect |
| 195. C2×D8 | C2×D97 | semidirect |
| 209. #108 | C2×D97 | semidirect |
| 213. #100 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261531 | 2 |
| C2×#15690829 | 2 |
| #131×D97 | 2 |
| #20261011 | 2 |
| #20261010 | 2 |
| #20261002 | 2 |
| #20260997 | 2 |
| #20260996 | 2 |
| #108×D97 | 2 |
| #20260716 | 2 |
| #472×C97 | 2 |
| #3067 | 97 |