Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16862253 | C2 | semidirect |
| 3. #22553876 | C2 | semidirect |
| 4. #22553563 | C2 | semidirect |
| 5. #22553560 | C2 | semidirect |
| 6. #22553546 | C2 | semidirect |
| 7. #22553543 | C2 | semidirect |
| 8. #22553352 | C2 | semidirect |
| 9. #22553308 | C2 | semidirect |
| 10. C2×#16862166 | C2 | semidirect |
| 11. #537×C131 | C2 | semidirect |
| 18. C2×#14523497 | C22 | semidirect |
| 20. C22×C131⋊C8 | C22 | semidirect |
| 27. #16862179 | C22 | semidirect |
| 28. #16862177 | C22 | semidirect |
| 29. #16862170 | C22 | semidirect |
| 30. #16862170 | C22 | semidirect |
| 31. #16862167 | C22 | semidirect |
| 32. #16862167 | C22 | semidirect |
| 38. C22⋊Q8×C131 | C22 | semidirect |
| 41. #121×C131 | C22 | semidirect |
| 53. #14523497 | D4 | semidirect |
| 151. C131 | #3062 | semidirect |
| 155. #537 | D131 | semidirect |
| 178. C22⋊Q8 | C2×D131 | semidirect |
| 183. #121 | 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 |
| C2×#16862253 | 2 |
| #22553876 | 2 |
| #22553563 | 2 |
| #22553560 | 2 |
| #22553546 | 2 |
| #22553543 | 2 |
| #22553352 | 2 |
| #22553308 | 2 |
| C2×#16862166 | 2 |
| #537×C131 | 2 |
| #3062 | 131 |