Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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. #16811323 | C2 | semidirect |
| 2. #16811025 | C2 | semidirect |
| 3. #16810945 | C2 | semidirect |
| 4. #16810935 | C2 | semidirect |
| 5. #16810923 | C2 | semidirect |
| 6. #16810873 | C2 | semidirect |
| 7. #16810702 | C2 | semidirect |
| 8. #16810664 | C2 | semidirect |
| 9. C4×D8×C53 | C2 | semidirect |
| 109. C4×D8 | D53 | semidirect |
| 112. C53 | #3355 | semidirect |