Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
396 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22554023 | C2 | semidirect |
| 2. #22553982 | C2 | semidirect |
| 3. #22553675 | C2 | semidirect |
| 4. #22553610 | C2 | semidirect |
| 5. #22553599 | C2 | semidirect |
| 6. #22553506 | C2 | semidirect |
| 7. #22553504 | C2 | semidirect |
| 8. #22553442 | C2 | semidirect |
| 9. #22553421 | C2 | semidirect |
| 10. C4×D1048 | C2 | semidirect |
| 11. #486×C131 | C2 | semidirect |
| 80. D524 | #41 | semidirect |
| 129. C131 | #3366 | semidirect |
| 134. #486 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554023 | 2 |
| #22553982 | 2 |
| #22553675 | 2 |
| #22553610 | 2 |
| #22553599 | 2 |
| #22553506 | 2 |
| #22553504 | 2 |
| #22553442 | 2 |
| #22553421 | 2 |
| C4×D1048 | 2 |
| #486×C131 | 2 |
| #3366 | 131 |