Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 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. #22554047 | C2 | semidirect |
| 2. #22554023 | C2 | semidirect |
| 3. #22553668 | C2 | semidirect |
| 4. #22553660 | C2 | semidirect |
| 5. #22553615 | C2 | semidirect |
| 6. #22553530 | C2 | semidirect |
| 8. #22553436 | C2 | semidirect |
| 9. C4×#14523500 | C2 | semidirect |
| 10. #22553394 | C2 | semidirect |
| 11. #477×C131 | C2 | semidirect |
| 122. C131 | #3361 | semidirect |
| 129. #477 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554047 | 2 |
| #22554023 | 2 |
| #22553668 | 2 |
| #22553660 | 2 |
| #22553615 | 2 |
| #22553530 | 2 |
| #22553508 | 2 |
| #22553436 | 2 |
| C4×#14523500 | 2 |
| #22553394 | 2 |
| #477×C131 | 2 |
| #3361 | 131 |