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×D776 | C2 | semidirect |
| 2. C2×#15690816 | C2 | semidirect |
| 3. #20261304 | C2 | semidirect |
| 4. #20260989 | C2 | semidirect |
| 5. #20260972 | C2 | semidirect |
| 6. #20260739 | C2 | semidirect |
| 7. #427×C97 | C2 | semidirect |
| 15. C2×#13095494 | C22 | semidirect |
| 16. C2×C8×D97 | C22 | semidirect |
| 19. #15690785 | C22 | semidirect |
| 21. #15690730 | C22 | semidirect |
| 24. #107×C97 | C22 | semidirect |
| 25. #106×C97 | C22 | semidirect |
| 46. C2×C8×C97 | D4 | semidirect |
| 94. C97 | #3058 | semidirect |
| 100. #427 | D97 | semidirect |
| 117. #107 | C2×D97 | semidirect |
| 118. #106 | C2×D97 | semidirect |
| 139. C2×C8 | D388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D776 | 2 |
| C2×#15690816 | 2 |
| #20261304 | 2 |
| #20260989 | 2 |
| #20260972 | 2 |
| #20260739 | 2 |
| #427×C97 | 2 |
| #3058 | 97 |