Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22554019 | C2 | semidirect |
| 3. #22553668 | C2 | semidirect |
| 4. #22553659 | C2 | semidirect |
| 5. #22553611 | C2 | semidirect |
| 6. #22553607 | C2 | semidirect |
| 7. #22553529 | C2 | semidirect |
| 9. C8×Dic262 | C2 | semidirect |
| 10. #22553392 | C2 | semidirect |
| 11. C4×SD16×C131 | C2 | semidirect |
| 122. C131 | #3361 | semidirect |
| 133. C4×SD16 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554047 | 2 |
| #22554019 | 2 |
| #22553668 | 2 |
| #22553659 | 2 |
| #22553611 | 2 |
| #22553607 | 2 |
| #22553529 | 2 |
| #22553507 | 2 |
| C8×Dic262 | 2 |
| #22553392 | 2 |
| C4×SD16×C131 | 2 |
| #3361 | 131 |