Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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×#16862271 | C2 | semidirect |
| 2. C2×#16862271 | C2 | semidirect |
| 3. #22554079 | C2 | semidirect |
| 4. #22553580 | C2 | semidirect |
| 5. #22553577 | C2 | semidirect |
| 6. #22553360 | C2 | semidirect |
| 7. #22553296 | C2 | semidirect |
| 8. C2×#16862162 | C2 | semidirect |
| 9. #575×C131 | C2 | semidirect |
| 16. C2×#14523500 | C22 | semidirect |
| 18. C2×#14523498 | C22 | semidirect |
| 20. #16862253 | C22 | semidirect |
| 25. #16862181 | C22 | semidirect |
| 26. #16862165 | C22 | semidirect |
| 27. #16862163 | C22 | semidirect |
| 28. #16862162 | C22 | semidirect |
| 32. #137×C131 | C22 | semidirect |
| 34. AGL(1,ℤ/8)×C131 | C22 | semidirect |
| 147. C131 | #3068 | semidirect |
| 149. #575 | D131 | semidirect |
| 162. #137 | C2×D131 | semidirect |
| 168. AGL(1,ℤ/8) | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862271 | 2 |
| #22554079 | 2 |
| #22553580 | 2 |
| #22553577 | 2 |
| #22553360 | 2 |
| #22553296 | 2 |
| C2×#16862162 | 2 |
| #575×C131 | 2 |
| #3068 | 131 |