Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22554027 | C2 | semidirect |
| 2. #22553662 | C2 | semidirect |
| 3. #22553650 | C2 | semidirect |
| 4. #22553602 | C2 | semidirect |
| 5. #22553543 | C2 | semidirect |
| 6. #22553514 | C2 | semidirect |
| 7. #22553457 | C2 | semidirect |
| 8. C4×#14523498 | C2 | semidirect |
| 9. D4×C131⋊C8 | C2 | semidirect |
| 10. #22553308 | C2 | semidirect |
| 11. #547×C131 | C2 | semidirect |
| 130. C131 | #3303 | semidirect |
| 133. #547 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554027 | 2 |
| #22553662 | 2 |
| #22553650 | 2 |
| #22553602 | 2 |
| #22553543 | 2 |
| #22553514 | 2 |
| #22553457 | 2 |
| C4×#14523498 | 2 |
| D4×C131⋊C8 | 2 |
| #22553308 | 2 |
| #547×C131 | 2 |
| #3303 | 131 |