Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×Dic212 | C2 | semidirect |
| 4. C2×#13133182 | C2 | semidirect |
| 5. #16810844 | C2 | direct (N × H) |
| 6. C2×#13133146 | C2 | semidirect |
| 7. C2×#13133140 | C2 | semidirect |
| 12. C2×Dic212 | C22 | semidirect |
| 19. #13133182 | C22 | semidirect |
| 25. #13133146 | C22 | semidirect |
| 26. #13133140 | C22 | semidirect |
| 112. C2×C53 | #464 | semidirect |
| 124. C53 | C2×#464 | semidirect |
| 227. C2 | #16810844 | direct (N × H) |