Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
468 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 468 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×#16862276 | C2 | semidirect |
| 3. C22×#14523502 | C2 | semidirect |
| 4. #22553575 | C2 | direct (N × H) |
| 5. C2×#16862182 | C2 | semidirect |
| 6. C2×#16862164 | C2 | semidirect |
| 7. C2×#16862162 | C2 | semidirect |
| 8. C2×#131×C131 | C2 | semidirect |
| 12. #16862276 | C22 | semidirect |
| 19. C2×#14523502 | C22 | semidirect |
| 25. #16862182 | C22 | semidirect |
| 26. #16862164 | C22 | semidirect |
| 27. #16862162 | C22 | semidirect |
| 30. #131×C131 | C22 | semidirect |
| 135. C2×C131 | #471 | semidirect |
| 138. C131 | C2×#471 | semidirect |
| 143. C2×#131 | D131 | semidirect |
| 164. #131 | C2×D131 | semidirect |
| 275. C2 | #22553575 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862276 | 2 |
| C2×#16862271 | 2 |
| C22×#14523502 | 2 |
| #22553575 | 2 |
| C2×#16862182 | 2 |
| C2×#16862164 | 2 |
| C2×#16862162 | 2 |
| C2×#131×C131 | 2 |
| C2×#471 | 131 |