Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
360 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 3. #16810632 | C2 | semidirect |
| 5. #16810384 | C2 | semidirect |
| 6. #16810382 | C2 | semidirect |
| 7. C53×#419 | C2 | semidirect |
| 11. #13133206 | C4 | semidirect |
| 30. C2×Q8×C53 | C2×C4 | semidirect |
| 53. C4×Dic53 | C2×C4 | semidirect |
| 111. #419 | D53 | semidirect |
| 115. C53 | #1885 | semidirect |
| 138. C2×Q8 | C4×D53 | semidirect |