Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
362 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 362 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. #22553666 | C2 | semidirect |
| 3. #22553658 | C2 | semidirect |
| 4. #22553612 | C2 | semidirect |
| 5. #22553607 | C2 | semidirect |
| 6. #22553524 | C2 | semidirect |
| 8. Q8×C131⋊C8 | C2 | semidirect |
| 9. C4×#14523500 | C2 | semidirect |
| 10. C4×#14523498 | C2 | semidirect |
| 11. #559×C131 | C2 | semidirect |
| 122. C131 | #3361 | semidirect |
| 124. #559 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554022 | 2 |
| #22553666 | 2 |
| #22553658 | 2 |
| #22553612 | 2 |
| #22553607 | 2 |
| #22553524 | 2 |
| #22553504 | 2 |
| Q8×C131⋊C8 | 2 |
| C4×#14523500 | 2 |
| C4×#14523498 | 2 |
| #559×C131 | 2 |
| #3361 | 131 |