Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
446 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 137 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×#16862277 | C2 | semidirect |
| 3. #22554078 | C2 | semidirect |
| 4. #22553584 | C2 | semidirect |
| 5. #22553572 | C2 | semidirect |
| 6. #22553361 | C2 | semidirect |
| 7. #22553296 | C2 | semidirect |
| 8. C2×#16862165 | C2 | semidirect |
| 9. C2×#137×C131 | C2 | semidirect |
| 26. #16862182 | C22 | semidirect |
| 27. #16862165 | C22 | semidirect |
| 28. #16862165 | C22 | semidirect |
| 29. #16862163 | C22 | semidirect |
| 34. C2×Q16×C131 | C22 | semidirect |
| 35. C2×SD16×C131 | C22 | semidirect |
| 142. C131 | #3069 | semidirect |
| 146. C2×#137 | D131 | semidirect |
| 166. C2×Q16 | C2×D131 | semidirect |
| 168. C2×SD16 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554110 | 2 |
| C2×#16862277 | 2 |
| #22554078 | 2 |
| #22553584 | 2 |
| #22553572 | 2 |
| #22553361 | 2 |
| #22553296 | 2 |
| C2×#16862165 | 2 |
| C2×#137×C131 | 2 |
| #3069 | 131 |