Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 312 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 |
|---|---|---|
| 4. C2×#13133142 | C2 | semidirect |
| 5. C2×#13133135 | C2 | semidirect |
| 6. #16810391 | C2 | semidirect |
| 7. C53×#341 | C2 | semidirect |
| 11. #13133250 | C4 | semidirect |
| 123. #341 | D53 | semidirect |
| 124. C53 | #1908 | semidirect |