Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16862274 | C2 | semidirect |
| 2. C2×#16862254 | C2 | semidirect |
| 3. #22553893 | C2 | semidirect |
| 4. #22553881 | C2 | semidirect |
| 5. #22553566 | C2 | semidirect |
| 6. #22553559 | C2 | semidirect |
| 7. #22553549 | C2 | semidirect |
| 8. #22553542 | C2 | semidirect |
| 9. #22553306 | C2 | semidirect |
| 10. C2×#16862166 | C2 | semidirect |
| 11. #428×C131 | C2 | semidirect |
| 19. C2×#14523496 | C22 | semidirect |
| 21. C2×C8×D131 | C22 | semidirect |
| 25. #16862226 | C22 | semidirect |
| 29. #16862221 | C22 | semidirect |
| 32. #16862169 | C22 | semidirect |
| 33. #16862169 | C22 | semidirect |
| 36. #16862166 | C22 | semidirect |
| 37. #16862166 | C22 | semidirect |
| 41. #107×C131 | C22 | semidirect |
| 42. #106×C131 | C22 | semidirect |
| 77. M16×C131 | D4 | semidirect |
| 151. C131 | #3062 | semidirect |
| 161. #428 | D131 | semidirect |
| 187. #107 | C2×D131 | semidirect |
| 188. #106 | C2×D131 | semidirect |
| 220. M16 | D524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862274 | 2 |
| C2×#16862254 | 2 |
| #22553893 | 2 |
| #22553881 | 2 |
| #22553566 | 2 |
| #22553559 | 2 |
| #22553549 | 2 |
| #22553542 | 2 |
| #22553306 | 2 |
| C2×#16862166 | 2 |
| #428×C131 | 2 |
| #3062 | 131 |