Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
468 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 468 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 |
|---|---|---|
| 1. C2×#13133250 | C2 | semidirect |
| 3. C22×#11719923 | C2 | semidirect |
| 4. C2×#13133225 | C2 | semidirect |
| 5. #16810885 | C2 | direct (N × H) |
| 6. C2×#13133152 | C2 | semidirect |
| 7. C2×#13133135 | C2 | semidirect |
| 8. C2×#100×C53 | C2 | semidirect |
| 12. #13133250 | C22 | semidirect |
| 21. C2×#11719923 | C22 | semidirect |
| 24. #13133225 | C22 | semidirect |
| 29. #13133152 | C22 | semidirect |
| 30. #13133135 | C22 | semidirect |
| 34. #100×C53 | C22 | semidirect |
| 136. C2×C53 | #471 | semidirect |
| 146. C2×#100 | D53 | semidirect |
| 147. C53 | C2×#471 | semidirect |
| 173. #100 | C2×D53 | semidirect |
| 275. C2 | #16810885 | direct (N × H) |