Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
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. #16811421 | C2 | semidirect |
| 2. C2×#13133243 | C2 | semidirect |
| 3. #16811390 | C2 | semidirect |
| 4. #16810891 | C2 | semidirect |
| 5. #16810884 | C2 | semidirect |
| 6. #16810671 | C2 | semidirect |
| 7. #16810605 | C2 | semidirect |
| 8. C2×#13133134 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C53 | C2 | semidirect |
| 12. #13133247 | C22 | semidirect |
| 16. #13133242 | C22 | semidirect |
| 18. C2×#11719923 | C22 | semidirect |
| 19. C2×#11719922 | C22 | semidirect |
| 21. #13133224 | C22 | semidirect |
| 26. #13133152 | C22 | semidirect |
| 27. #13133135 | C22 | semidirect |
| 28. #13133134 | C22 | semidirect |
| 29. #13133133 | C22 | semidirect |
| 150. C2×AGL(1,ℤ/8) | D53 | semidirect |
| 157. C53 | #3068 | semidirect |