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×#16862272 | C2 | semidirect |
| 2. C2×#16862266 | C2 | semidirect |
| 3. #22553792 | C2 | semidirect |
| 4. #22553531 | C2 | semidirect |
| 5. #22553524 | C2 | semidirect |
| 6. #22553509 | C2 | semidirect |
| 7. #22553504 | C2 | semidirect |
| 8. #22553339 | C2 | semidirect |
| 9. #22553313 | C2 | semidirect |
| 10. C2×#16862167 | C2 | semidirect |
| 11. #535×C131 | C2 | semidirect |
| 15. C2×#14523503 | C22 | semidirect |
| 17. C2×#14523501 | C22 | semidirect |
| 18. C2×#14523500 | C22 | semidirect |
| 20. C2×#14523498 | C22 | semidirect |
| 23. C4×Dic262 | C22 | semidirect |
| 24. C4×D524 | C22 | semidirect |
| 29. C4⋊(C131⋊C8) | C22 | semidirect |
| 30. C4⋊(C131⋊C8) | C22 | semidirect |
| 31. #16862170 | C22 | semidirect |
| 34. #16862167 | C22 | semidirect |
| 44. #14523513 | D4 | semidirect |
| 154. C131 | #3045 | semidirect |
| 158. #535 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862272 | 2 |
| C2×#16862266 | 2 |
| #22553792 | 2 |
| #22553531 | 2 |
| #22553524 | 2 |
| #22553509 | 2 |
| #22553504 | 2 |
| #22553339 | 2 |
| #22553313 | 2 |
| C2×#16862167 | 2 |
| #535×C131 | 2 |
| #3045 | 131 |