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. #22553641 | C2 | semidirect |
| 4. #22553603 | C2 | semidirect |
| 5. #22553602 | C2 | semidirect |
| 6. #22553514 | C2 | semidirect |
| 8. SD16×Dic131 | C2 | semidirect |
| 9. #22553397 | C2 | semidirect |
| 10. #22553364 | C2 | semidirect |
| 11. #461×C131 | C2 | semidirect |
| 15. #16862246 | C22 | semidirect |
| 19. Q8×Dic131 | C22 | semidirect |
| 30. #16862178 | C22 | semidirect |
| 31. #16862177 | C22 | semidirect |
| 32. C4⋊(C131⋊C8) | C22 | semidirect |
| 33. #16862170 | C22 | semidirect |
| 37. C8×Dic131 | C22 | semidirect |
| 39. C4⋊Q8×C131 | C22 | semidirect |
| 41. C4⋊C8×C131 | C22 | semidirect |
| 42. #103×C131 | C22 | semidirect |
| 104. C4×D131 | SD16 | semidirect |
| 146. C131 | #3101 | semidirect |
| 154. #461 | D131 | semidirect |
| 164. C4⋊Q8 | C2×D131 | semidirect |
| 183. C4⋊C8 | C2×D131 | semidirect |
| 185. #103 | 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 |
| #22553641 | 2 |
| #22553603 | 2 |
| #22553602 | 2 |
| #22553514 | 2 |
| #22553461 | 2 |
| SD16×Dic131 | 2 |
| #22553397 | 2 |
| #22553364 | 2 |
| #461×C131 | 2 |
| #3101 | 131 |