Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22553792 | C2 | semidirect |
| 3. #22553635 | C2 | semidirect |
| 4. #22553634 | C2 | semidirect |
| 5. #22553629 | C2 | semidirect |
| 6. #22553624 | C2 | semidirect |
| 7. #22553354 | C2 | semidirect |
| 8. #22553348 | C2 | semidirect |
| 9. C2×#16862167 | C2 | semidirect |
| 10. #22553280 | C2 | semidirect |
| 11. #418×C131 | C2 | semidirect |
| 23. #16862204 | C22 | semidirect |
| 25. C4⋊C4×D131 | C22 | semidirect |
| 26. #16862180 | C22 | semidirect |
| 27. #16862179 | C22 | semidirect |
| 28. #16862179 | C22 | semidirect |
| 29. #16862178 | C22 | semidirect |
| 30. #16862177 | C22 | semidirect |
| 31. #16862177 | C22 | semidirect |
| 34. (C2×D131)⋊C8 | C22 | semidirect |
| 35. (C2×D131)⋊C8 | C22 | semidirect |
| 134. C131 | #3096 | semidirect |
| 144. #418 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553879 | 2 |
| #22553792 | 2 |
| #22553635 | 2 |
| #22553634 | 2 |
| #22553629 | 2 |
| #22553624 | 2 |
| #22553354 | 2 |
| #22553348 | 2 |
| C2×#16862167 | 2 |
| #22553280 | 2 |
| #418×C131 | 2 |
| #3096 | 131 |