Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 3. #22553646 | C2 | semidirect |
| 4. #22553604 | C2 | semidirect |
| 5. #22553552 | C2 | semidirect |
| 6. #22553519 | C2 | semidirect |
| 7. #22553469 | C2 | semidirect |
| 8. C4×Dic524 | C2 | semidirect |
| 10. #103×D131 | C2 | semidirect |
| 11. #487×C131 | C2 | semidirect |
| 82. D524 | Q16 | semidirect |
| 122. C131 | #3299 | semidirect |
| 126. #487 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554023 | 2 |
| #22553977 | 2 |
| #22553646 | 2 |
| #22553604 | 2 |
| #22553552 | 2 |
| #22553519 | 2 |
| #22553469 | 2 |
| C4×Dic524 | 2 |
| C8×D524 | 2 |
| #103×D131 | 2 |
| #487×C131 | 2 |
| #3299 | 131 |