Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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. C22×D1048 | C2 | semidirect |
| 3. #22553881 | C2 | semidirect |
| 4. #22553786 | C2 | semidirect |
| 5. #22553528 | C2 | semidirect |
| 6. #22553508 | C2 | semidirect |
| 7. #22553318 | C2 | semidirect |
| 8. #22553309 | C2 | semidirect |
| 9. #424×C131 | C2 | semidirect |
| 14. C2×#14523502 | C22 | semidirect |
| 17. C2×D1048 | C22 | semidirect |
| 18. #16862243 | C22 | semidirect |
| 19. #16862234 | C22 | semidirect |
| 22. C4×D524 | C22 | semidirect |
| 26. #16862171 | C22 | semidirect |
| 27. #16862168 | C22 | semidirect |
| 28. #16862168 | C22 | semidirect |
| 32. C4⋊C8×C131 | C22 | semidirect |
| 44. C2×D524 | D4 | semidirect |
| 121. C131 | #3041 | semidirect |
| 129. #424 | D131 | semidirect |
| 151. C4⋊C8 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862274 | 2 |
| C22×D1048 | 2 |
| #22553881 | 2 |
| #22553786 | 2 |
| #22553528 | 2 |
| #22553508 | 2 |
| #22553318 | 2 |
| #22553309 | 2 |
| #424×C131 | 2 |
| #3041 | 131 |