Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
448 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 127 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. #22553644 | C2 | semidirect |
| 4. #22553599 | C2 | semidirect |
| 5. #22553518 | C2 | semidirect |
| 6. #22553517 | C2 | semidirect |
| 8. #22553403 | C2 | semidirect |
| 9. #22553399 | C2 | semidirect |
| 10. #22553364 | C2 | semidirect |
| 11. #476×C131 | C2 | semidirect |
| 16. #16862246 | C22 | semidirect |
| 21. #16862211 | C22 | semidirect |
| 31. #16862177 | C22 | semidirect |
| 32. C4⋊(C131⋊C8) | C22 | semidirect |
| 33. #16862171 | C22 | semidirect |
| 34. #16862169 | C22 | semidirect |
| 37. C8×Dic131 | C22 | semidirect |
| 38. C4⋊Q8×C131 | C22 | semidirect |
| 40. #106×C131 | C22 | semidirect |
| 41. C4⋊C8×C131 | C22 | semidirect |
| 105. C4×D131 | SD16 | semidirect |
| 146. C131 | #3101 | semidirect |
| 152. #476 | D131 | semidirect |
| 164. C4⋊Q8 | C2×D131 | semidirect |
| 181. #106 | C2×D131 | semidirect |
| 183. C4⋊C8 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553867 | 2 |
| C4×D4×D131 | 2 |
| #22553644 | 2 |
| #22553599 | 2 |
| #22553518 | 2 |
| #22553517 | 2 |
| #22553464 | 2 |
| #22553403 | 2 |
| #22553399 | 2 |
| #22553364 | 2 |
| #476×C131 | 2 |
| #3101 | 131 |