Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#16862273 | C2 | semidirect |
| 2. #22553863 | C2 | semidirect |
| 3. C4×D4×D131 | C2 | semidirect |
| 4. #22553530 | C2 | semidirect |
| 5. #22553529 | C2 | semidirect |
| 6. #22553514 | C2 | semidirect |
| 7. #22553508 | C2 | semidirect |
| 8. #22553507 | C2 | semidirect |
| 9. #22553334 | C2 | semidirect |
| 10. #22553312 | C2 | semidirect |
| 11. #461×C131 | C2 | semidirect |
| 20. #16862243 | C22 | semidirect |
| 21. #16862235 | C22 | semidirect |
| 34. C4⋊(C131⋊C8) | C22 | semidirect |
| 35. Dic131⋊C8 | C22 | semidirect |
| 36. #16862170 | C22 | semidirect |
| 37. #16862168 | C22 | semidirect |
| 38. #16862166 | C22 | semidirect |
| 40. C4⋊Q8×C131 | C22 | semidirect |
| 42. C4⋊C8×C131 | C22 | semidirect |
| 43. #103×C131 | C22 | semidirect |
| 54. D4×D131 | D4 | semidirect |
| 146. C4×C131 | AGL(1,ℤ/8) | semidirect |
| 160. C131 | #3036 | semidirect |
| 168. #461 | D131 | semidirect |
| 182. C4⋊Q8 | C2×D131 | semidirect |
| 200. C4⋊C8 | C2×D131 | semidirect |
| 202. #103 | C2×D131 | semidirect |
| 311. C4 | #16862273 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862273 | 2 |
| #22553863 | 2 |
| C4×D4×D131 | 2 |
| #22553530 | 2 |
| #22553529 | 2 |
| #22553514 | 2 |
| #22553508 | 2 |
| #22553507 | 2 |
| #22553334 | 2 |
| #22553312 | 2 |
| #461×C131 | 2 |
| #3036 | 131 |