Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #16811338 | C2 | semidirect |
| 2. #16811278 | C2 | semidirect |
| 3. #16811021 | C2 | semidirect |
| 4. #16810946 | C2 | semidirect |
| 5. #16810940 | C2 | semidirect |
| 6. #16810913 | C2 | semidirect |
| 7. #16810903 | C2 | semidirect |
| 8. #16810873 | C2 | semidirect |
| 9. #16810702 | C2 | semidirect |
| 10. #16810664 | C2 | semidirect |
| 11. C4×D8×C53 | C2 | semidirect |
| 100. C8×C53 | #41 | semidirect |
| 136. C4×D8 | D53 | semidirect |
| 139. C53 | #3354 | semidirect |
| 229. C8 | #11719945 | semidirect |