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. #22553636 | C2 | semidirect |
| 3. #22553636 | C2 | semidirect |
| 4. #22553630 | C2 | semidirect |
| 5. #22553625 | C2 | semidirect |
| 6. #22553352 | C2 | semidirect |
| 7. #22553348 | C2 | semidirect |
| 8. #22553316 | C2 | semidirect |
| 9. C2×#16862166 | C2 | semidirect |
| 10. #22553279 | C2 | semidirect |
| 11. #520×C131 | C2 | semidirect |
| 21. #16862179 | C22 | semidirect |
| 22. #16862179 | C22 | semidirect |
| 23. #16862179 | C22 | semidirect |
| 24. #16862177 | C22 | semidirect |
| 25. #16862177 | C22 | semidirect |
| 26. #16862177 | C22 | semidirect |
| 31. C22⋊(C131⋊C8) | C22 | semidirect |
| 32. C22⋊(C131⋊C8) | C22 | semidirect |
| 38. #117×C131 | C22 | semidirect |
| 40. C2×C4⋊C4×C131 | C22 | semidirect |
| 134. C131 | #3096 | semidirect |
| 137. #520 | D131 | semidirect |
| 161. #117 | C2×D131 | semidirect |
| 163. C2×C4⋊C4 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553876 | 2 |
| #22553636 | 2 |
| #22553630 | 2 |
| #22553625 | 2 |
| #22553352 | 2 |
| #22553348 | 2 |
| #22553316 | 2 |
| C2×#16862166 | 2 |
| #22553279 | 2 |
| #520×C131 | 2 |
| #3096 | 131 |