Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
120 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 23 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 |
|---|---|---|
| 2. #16810416 | C2 | semidirect |
| 3. C53×#353 | C2 | semidirect |
| 6. #13133214 | C4 | semidirect |
| 8. C4×#88322 | C4 | semidirect |
| 55. #353 | D53 | semidirect |
| 56. C53 | #1408 | semidirect |