Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 350 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. #22554036 | C2 | semidirect |
| 2. #22554023 | C2 | semidirect |
| 3. #22553668 | C2 | semidirect |
| 4. #22553621 | C2 | semidirect |
| 5. #22553599 | C2 | semidirect |
| 7. #22553514 | C2 | semidirect |
| 8. C8×Dic262 | C2 | semidirect |
| 9. #22553397 | C2 | semidirect |
| 11. #487×C131 | C2 | semidirect |
| 120. C131 | #3360 | semidirect |
| 125. #487 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554036 | 2 |
| #22554023 | 2 |
| #22553668 | 2 |
| #22553621 | 2 |
| #22553599 | 2 |
| #22553530 | 2 |
| #22553514 | 2 |
| C8×Dic262 | 2 |
| #22553397 | 2 |
| C4×D1048 | 2 |
| #487×C131 | 2 |
| #3360 | 131 |