Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
446 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 2. C2×#16862279 | C2 | semidirect |
| 3. C2×#16862276 | C2 | semidirect |
| 4. #22553587 | C2 | semidirect |
| 5. #22553575 | C2 | semidirect |
| 6. #22553361 | C2 | semidirect |
| 7. #22553294 | C2 | semidirect |
| 8. C2×#16862164 | C2 | semidirect |
| 9. #568×C131 | C2 | semidirect |
| 21. C2×Dic524 | C22 | semidirect |
| 23. C2×#14523502 | C22 | semidirect |
| 27. #16862182 | C22 | semidirect |
| 28. #16862164 | C22 | semidirect |
| 29. #16862164 | C22 | semidirect |
| 30. #16862162 | C22 | semidirect |
| 142. C131 | #3069 | semidirect |
| 147. #568 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554110 | 2 |
| C2×#16862279 | 2 |
| C2×#16862276 | 2 |
| #22553587 | 2 |
| #22553575 | 2 |
| #22553361 | 2 |
| #22553294 | 2 |
| C2×#16862164 | 2 |
| #568×C131 | 2 |
| #3069 | 131 |