Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
994 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 157 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. C23×D524 | C2 | semidirect |
| 2. C2×#16862271 | C2 | semidirect |
| 3. #22553462 | C2 | semidirect |
| 4. #22553445 | C2 | semidirect |
| 5. #22553316 | C2 | semidirect |
| 6. #22553276 | C2 | semidirect |
| 7. #525×C131 | C2 | semidirect |
| 15. C2×#14523500 | C22 | semidirect |
| 16. C2×#14523498 | C22 | semidirect |
| 17. C2×#14523497 | C22 | semidirect |
| 18. #16862166 | C22 | semidirect |
| 19. C22⋊(C131⋊C8) | C22 | semidirect |
| 20. C2×#41×C131 | C22 | semidirect |
| 23. C22⋊Q8×C131 | C22 | semidirect |
| 24. #121×C131 | C22 | semidirect |
| 27. #117×C131 | C22 | semidirect |
| 38. C2×D524 | D4 | semidirect |
| 43. C2×C131⋊C8 | C23 | semidirect |
| 46. C2×Q8×C131 | C23 | semidirect |
| 49. C2×D4×C131 | C23 | semidirect |
| 57. C4⋊C4×C131 | C23 | semidirect |
| 100. C22×C131 | AGL(1,ℤ/8) | semidirect |
| 117. C131 | #3003 | semidirect |
| 121. #525 | D131 | semidirect |
| 127. C2×#41 | C2×D131 | semidirect |
| 139. C22⋊Q8 | C2×D131 | semidirect |
| 140. #121 | C2×D131 | semidirect |
| 143. #117 | C2×D131 | semidirect |
| 152. C2×Q8 | C22×D131 | semidirect |
| 163. C2×D4 | C22×D131 | semidirect |
| 175. C4⋊C4 | C22×D131 | semidirect |
| 222. C22 | #16862271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D524 | 2 |
| C2×#16862271 | 2 |
| #22553462 | 2 |
| #22553445 | 2 |
| #22553316 | 2 |
| #22553276 | 2 |
| #525×C131 | 2 |
| #3003 | 131 |