Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
448 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×#11719925 | C2 | semidirect |
| 5. #16810897 | C2 | direct (N × H) |
| 6. C2×#13133152 | C2 | semidirect |
| 7. C2×#13133135 | C2 | semidirect |
| 8. C2×#101×C53 | C2 | semidirect |
| 20. C2×#11719925 | C22 | semidirect |
| 29. #13133152 | C22 | semidirect |
| 30. #13133135 | C22 | semidirect |
| 34. #101×C53 | C22 | semidirect |
| 131. C2×C53 | #473 | semidirect |
| 141. C2×#101 | D53 | semidirect |
| 142. C53 | C2×#473 | semidirect |
| 168. #101 | C2×D53 | semidirect |
| 265. C2 | #16810897 | direct (N × H) |