Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
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. #22554022 | C2 | semidirect |
| 2. #22553984 | C2 | semidirect |
| 3. #22553677 | C2 | semidirect |
| 4. #22553659 | C2 | semidirect |
| 5. #22553613 | C2 | semidirect |
| 6. #22553603 | C2 | semidirect |
| 7. #22553508 | C2 | semidirect |
| 8. #22553508 | C2 | semidirect |
| 9. #22553425 | C2 | semidirect |
| 10. C4×D1048 | C2 | semidirect |
| 11. #446×C131 | C2 | semidirect |
| 87. D524 | #41 | semidirect |
| 129. C131 | #3366 | semidirect |
| 139. #446 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554022 | 2 |
| #22553984 | 2 |
| #22553677 | 2 |
| #22553659 | 2 |
| #22553613 | 2 |
| #22553603 | 2 |
| #22553508 | 2 |
| #22553425 | 2 |
| C4×D1048 | 2 |
| #446×C131 | 2 |
| #3366 | 131 |