Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
278 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 69 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. #16810414 | C2 | direct (N × H) |
| 5. C23×Dic53 | C4 | semidirect |
| 8. #13133198 | C4 | semidirect |
| 13. C2×C22⋊Dic53 | C4 | semidirect |
| 35. C22×Dic53 | C2×C4 | semidirect |
| 44. C22⋊Dic53 | C2×C4 | semidirect |
| 104. C2×C53 | #352 | semidirect |
| 110. C53 | C2×#352 | semidirect |
| 209. C2 | #16810414 | direct (N × H) |