Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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. C22×#14523502 | C2 | semidirect |
| 2. C2×#16862252 | C2 | semidirect |
| 3. #22553888 | C2 | semidirect |
| 5. #22553559 | C2 | semidirect |
| 6. #22553542 | C2 | semidirect |
| 7. #22553320 | C2 | semidirect |
| 8. #22553316 | C2 | semidirect |
| 9. #427×C131 | C2 | semidirect |
| 18. C2×#14523496 | C22 | semidirect |
| 19. C2×C8×D131 | C22 | semidirect |
| 25. #16862226 | C22 | semidirect |
| 28. #16862169 | C22 | semidirect |
| 33. #107×C131 | C22 | semidirect |
| 34. #106×C131 | C22 | semidirect |
| 62. C2×C8×C131 | D4 | semidirect |
| 120. C131 | #3057 | semidirect |
| 128. #427 | D131 | semidirect |
| 152. #107 | C2×D131 | semidirect |
| 153. #106 | C2×D131 | semidirect |
| 180. C2×C8 | D524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523502 | 2 |
| C2×#16862252 | 2 |
| #22553888 | 2 |
| #22553881 | 2 |
| #22553559 | 2 |
| #22553542 | 2 |
| #22553320 | 2 |
| #22553316 | 2 |
| #427×C131 | 2 |
| #3057 | 131 |