Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22553795 | C2 | semidirect |
| 3. #22553637 | C2 | semidirect |
| 4. #22553637 | C2 | semidirect |
| 5. #22553631 | C2 | semidirect |
| 6. #22553626 | C2 | semidirect |
| 7. #22553354 | C2 | semidirect |
| 8. #22553350 | C2 | semidirect |
| 9. #22553318 | C2 | semidirect |
| 10. C2×#16862168 | C2 | semidirect |
| 11. #408×C131 | C2 | semidirect |
| 23. #16862205 | C22 | semidirect |
| 25. C2×C4⋊Dic131 | C22 | semidirect |
| 26. #16862180 | C22 | semidirect |
| 27. #16862180 | C22 | semidirect |
| 28. #16862180 | C22 | semidirect |
| 29. #16862178 | C22 | semidirect |
| 30. #16862178 | C22 | semidirect |
| 31. #16862178 | C22 | semidirect |
| 39. C22⋊C8×C131 | C22 | semidirect |
| 40. C22⋊C8×C131 | C22 | semidirect |
| 134. C131 | #3096 | semidirect |
| 146. #408 | D131 | semidirect |
| 174. C22⋊C8 | C2×D131 | semidirect |
| 175. C22⋊C8 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553876 | 2 |
| #22553795 | 2 |
| #22553637 | 2 |
| #22553631 | 2 |
| #22553626 | 2 |
| #22553354 | 2 |
| #22553350 | 2 |
| #22553318 | 2 |
| C2×#16862168 | 2 |
| #408×C131 | 2 |
| #3096 | 131 |