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. #22553652 | C2 | semidirect |
| 4. #22553608 | C2 | semidirect |
| 5. #22553602 | C2 | semidirect |
| 6. #22553519 | C2 | semidirect |
| 8. #22553416 | C2 | semidirect |
| 9. #22553413 | C2 | semidirect |
| 10. #22553368 | C2 | semidirect |
| 11. #461×C131 | C2 | semidirect |
| 136. C131 | #3116 | semidirect |
| 144. #461 | 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 |
| #22553652 | 2 |
| #22553608 | 2 |
| #22553602 | 2 |
| #22553519 | 2 |
| #22553471 | 2 |
| #22553416 | 2 |
| #22553413 | 2 |
| #22553368 | 2 |
| #461×C131 | 2 |
| #3116 | 131 |