Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13133264 | C2 | semidirect |
| 2. C2×#13133245 | C2 | semidirect |
| 3. C2×#13133242 | C2 | semidirect |
| 4. C2×#13133205 | C2 | semidirect |
| 5. #16810797 | C2 | direct (N × H) |
| 6. C2×#13133145 | C2 | semidirect |
| 7. C2×#13133135 | C2 | semidirect |
| 8. C2×#104×C53 | C2 | semidirect |
| 12. #13133264 | C22 | semidirect |
| 22. #13133245 | C22 | semidirect |
| 24. #13133242 | C22 | semidirect |
| 31. #13133205 | C22 | semidirect |
| 33. #13133145 | C22 | semidirect |
| 34. #13133135 | C22 | semidirect |
| 38. #104×C53 | C22 | semidirect |
| 172. C2×C53 | #454 | semidirect |
| 182. C2×#104 | D53 | semidirect |
| 184. C53 | C2×#454 | semidirect |
| 213. #104 | C2×D53 | semidirect |
| 349. C2 | #16810797 | direct (N × H) |