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. #20261534 | C2 | semidirect |
| 2. C2×#15690833 | C2 | semidirect |
| 3. #131×D97 | C2 | semidirect |
| 4. #20261007 | C2 | semidirect |
| 5. #20261006 | C2 | semidirect |
| 6. #20261005 | C2 | semidirect |
| 7. #20261001 | C2 | semidirect |
| 8. #20261000 | C2 | semidirect |
| 9. #108×D97 | C2 | semidirect |
| 10. #20260718 | C2 | semidirect |
| 11. #473×C97 | C2 | semidirect |
| 25. C2×#13095498 | C22 | semidirect |
| 26. C2×D776 | C22 | semidirect |
| 37. #15690746 | C22 | semidirect |
| 38. #15690745 | C22 | semidirect |
| 39. #15690729 | C22 | semidirect |
| 40. #15690726 | C22 | semidirect |
| 41. #15690726 | C22 | semidirect |
| 43. C2×Q16×C97 | C22 | semidirect |
| 45. #108×C97 | C22 | semidirect |
| 46. #101×C97 | C22 | semidirect |
| 167. C97 | #3067 | semidirect |
| 172. #473 | D97 | semidirect |
| 193. C2×Q16 | C2×D97 | semidirect |
| 209. #108 | C2×D97 | semidirect |
| 211. #101 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261534 | 2 |
| C2×#15690833 | 2 |
| #131×D97 | 2 |
| #20261007 | 2 |
| #20261006 | 2 |
| #20261005 | 2 |
| #20261001 | 2 |
| #20261000 | 2 |
| #108×D97 | 2 |
| #20260718 | 2 |
| #473×C97 | 2 |
| #3067 | 97 |