Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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. #22553867 | C2 | semidirect |
| 3. #22553656 | C2 | semidirect |
| 4. #22553604 | C2 | semidirect |
| 5. #22553523 | C2 | semidirect |
| 6. #22553517 | C2 | semidirect |
| 8. #22553418 | C2 | semidirect |
| 9. #22553409 | C2 | semidirect |
| 10. #22553368 | C2 | semidirect |
| 11. #476×C131 | C2 | semidirect |
| 136. C131 | #3116 | semidirect |
| 142. #476 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553867 | 2 |
| C4×#14523512 | 2 |
| #22553656 | 2 |
| #22553604 | 2 |
| #22553523 | 2 |
| #22553517 | 2 |
| #22553475 | 2 |
| #22553418 | 2 |
| #22553409 | 2 |
| #22553368 | 2 |
| #476×C131 | 2 |
| #3116 | 131 |