Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
434 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 129 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. C4×#14523513 | C2 | semidirect |
| 2. #22553633 | C2 | semidirect |
| 3. #22553604 | C2 | semidirect |
| 4. #22553599 | C2 | semidirect |
| 5. #22553509 | C2 | semidirect |
| 6. #22553504 | C2 | semidirect |
| 7. #22553455 | C2 | semidirect |
| 8. C4×#14523501 | C2 | semidirect |
| 9. C4×#14523498 | C2 | semidirect |
| 10. #22553365 | C2 | semidirect |
| 11. #532×C131 | C2 | semidirect |
| 85. Dic262 | #41 | semidirect |
| 87. D524 | #41 | semidirect |
| 144. C131 | #3106 | semidirect |
| 146. #532 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14523513 | 2 |
| #22553633 | 2 |
| #22553604 | 2 |
| #22553599 | 2 |
| #22553509 | 2 |
| #22553504 | 2 |
| #22553455 | 2 |
| C4×#14523501 | 2 |
| C4×#14523498 | 2 |
| #22553365 | 2 |
| #532×C131 | 2 |
| #3106 | 131 |