Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
406 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 406 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. #16811343 | C2 | semidirect |
| 2. #16811294 | C2 | semidirect |
| 3. #16811011 | C2 | semidirect |
| 4. #16810996 | C2 | semidirect |
| 5. #16810837 | C2 | semidirect |
| 6. #16810828 | C2 | semidirect |
| 7. #16810822 | C2 | semidirect |
| 8. #16810818 | C2 | semidirect |
| 9. #16810753 | C2 | semidirect |
| 10. #16810722 | C2 | semidirect |
| 11. C4×D8×C53 | C2 | semidirect |
| 105. C8×C53 | #41 | semidirect |
| 143. C4×D8 | D53 | semidirect |
| 144. C53 | #3397 | semidirect |
| 239. C8 | #11719945 | semidirect |