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×#13133243 | C2 | semidirect |
| 3. C2×#13133204 | C2 | semidirect |
| 4. #16810794 | C2 | direct (N × H) |
| 5. C2×#13133144 | C2 | semidirect |
| 6. C2×#13133143 | C2 | semidirect |
| 7. C2×#13133135 | C2 | semidirect |
| 8. C2×AGL(1,ℤ/8)×C53 | C2 | semidirect |
| 12. #13133264 | C22 | semidirect |
| 21. #13133243 | C22 | semidirect |
| 26. #13133204 | C22 | semidirect |
| 29. #13133144 | C22 | semidirect |
| 30. #13133143 | C22 | semidirect |
| 31. #13133135 | C22 | semidirect |
| 35. AGL(1,ℤ/8)×C53 | C22 | semidirect |
| 173. C2×C53 | #454 | semidirect |
| 178. C2×AGL(1,ℤ/8) | D53 | semidirect |
| 184. C53 | C2×#454 | semidirect |
| 201. AGL(1,ℤ/8) | C2×D53 | semidirect |
| 349. C2 | #16810794 | direct (N × H) |