Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16862291 | C2 | semidirect |
| 2. C2×#16862274 | C2 | semidirect |
| 3. C22×#14523498 | C2 | semidirect |
| 4. #22553881 | C2 | semidirect |
| 5. #22553458 | C2 | semidirect |
| 6. #22553447 | C2 | semidirect |
| 7. #22553306 | C2 | semidirect |
| 8. #22553280 | C2 | semidirect |
| 9. #418×C131 | C2 | semidirect |
| 15. C2×#14523512 | C22 | semidirect |
| 16. C22×D524 | C22 | semidirect |
| 19. C2×D4×D131 | C22 | semidirect |
| 21. C2×#14523502 | C22 | semidirect |
| 22. C2×D1048 | C22 | semidirect |
| 24. C2×#14523498 | C22 | semidirect |
| 25. C22×C131⋊C8 | C22 | semidirect |
| 28. #16862221 | C22 | semidirect |
| 30. #16862169 | C22 | semidirect |
| 31. #16862166 | C22 | semidirect |
| 32. (C2×D131)⋊C8 | C22 | semidirect |
| 34. C2×M16×C131 | C22 | semidirect |
| 35. #117×C131 | C22 | semidirect |
| 36. #102×C131 | C22 | semidirect |
| 42. #14523513 | D4 | semidirect |
| 75. C2×D4×C131 | D4 | semidirect |
| 151. C131 | #3008 | semidirect |
| 159. #418 | D131 | semidirect |
| 178. C2×M16 | C2×D131 | semidirect |
| 184. #117 | C2×D131 | semidirect |
| 187. #102 | C2×D131 | semidirect |
| 218. C2×D4 | D524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862291 | 2 |
| C2×#16862274 | 2 |
| C22×#14523498 | 2 |
| #22553881 | 2 |
| #22553458 | 2 |
| #22553447 | 2 |
| #22553306 | 2 |
| #22553280 | 2 |
| #418×C131 | 2 |
| #3008 | 131 |