Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 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. #20261445 | C2 | semidirect |
| 2. #20261407 | C2 | semidirect |
| 3. #20261100 | C2 | semidirect |
| 4. #20261082 | C2 | semidirect |
| 5. #20261036 | C2 | semidirect |
| 6. #20261026 | C2 | semidirect |
| 7. #20260931 | C2 | semidirect |
| 8. #20260931 | C2 | semidirect |
| 9. #20260848 | C2 | semidirect |
| 10. C4×D776 | C2 | semidirect |
| 11. #446×C97 | C2 | semidirect |
| 95. D388 | #41 | semidirect |
| 130. C97 | #3366 | semidirect |
| 139. #446 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261445 | 2 |
| #20261407 | 2 |
| #20261100 | 2 |
| #20261082 | 2 |
| #20261036 | 2 |
| #20261026 | 2 |
| #20260931 | 2 |
| #20260848 | 2 |
| C4×D776 | 2 |
| #446×C97 | 2 |
| #3366 | 97 |