Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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. C22×#14523498 | C2 | semidirect |
| 2. #22553876 | C2 | semidirect |
| 3. #22553787 | C2 | semidirect |
| 4. #22553529 | C2 | semidirect |
| 5. #22553505 | C2 | semidirect |
| 6. #22553340 | C2 | semidirect |
| 7. #22553318 | C2 | semidirect |
| 8. #22553308 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C131 | C2 | semidirect |
| 14. #16862242 | C22 | semidirect |
| 15. #16862235 | C22 | semidirect |
| 19. D4×Dic131 | C22 | semidirect |
| 23. Dic131⋊C8 | C22 | semidirect |
| 24. #16862170 | C22 | semidirect |
| 25. #16862168 | C22 | semidirect |
| 26. #16862167 | C22 | semidirect |
| 30. C2×SD16×C131 | C22 | semidirect |
| 31. C2×D8×C131 | C22 | semidirect |
| 58. C2×D4×C131 | D4 | semidirect |
| 121. C131 | #3041 | semidirect |
| 123. C2×AGL(1,ℤ/8) | D131 | semidirect |
| 136. C2×SD16 | C2×D131 | semidirect |
| 139. C2×D8 | C2×D131 | semidirect |
| 168. C2×D4 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523498 | 2 |
| #22553876 | 2 |
| #22553787 | 2 |
| #22553529 | 2 |
| #22553505 | 2 |
| #22553340 | 2 |
| #22553318 | 2 |
| #22553308 | 2 |
| C2×AGL(1,ℤ/8)×C131 | 2 |
| #3041 | 131 |