Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 2. #22554041 | C2 | semidirect |
| 3. #22553668 | C2 | semidirect |
| 5. #22553615 | C2 | semidirect |
| 6. #22553597 | C2 | semidirect |
| 7. #22553536 | C2 | semidirect |
| 9. C8×Dic262 | C2 | semidirect |
| 10. #22553397 | C2 | semidirect |
| 11. C4×Q16×C131 | C2 | semidirect |
| 117. C131 | #3365 | semidirect |
| 128. C4×Q16 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554047 | 2 |
| #22554041 | 2 |
| #22553668 | 2 |
| #22553659 | 2 |
| #22553615 | 2 |
| #22553597 | 2 |
| #22553536 | 2 |
| #22553512 | 2 |
| C8×Dic262 | 2 |
| #22553397 | 2 |
| C4×Q16×C131 | 2 |
| #3365 | 131 |