Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
414 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#13133175 | C2 | semidirect |
| 3. #16810967 | C2 | semidirect |
| 4. #16810966 | C2 | semidirect |
| 5. #16810950 | C2 | semidirect |
| 6. #16810949 | C2 | semidirect |
| 7. #16810666 | C2 | semidirect |
| 8. #16810625 | C2 | semidirect |
| 9. #16810622 | C2 | semidirect |
| 10. #16810586 | C2 | semidirect |
| 11. C53×#428 | C2 | semidirect |
| 30. #13133150 | C22 | semidirect |
| 31. #13133148 | C22 | semidirect |
| 32. #13133142 | C22 | semidirect |
| 33. #13133140 | C22 | semidirect |
| 34. #13133139 | C22 | semidirect |
| 35. #13133137 | C22 | semidirect |
| 41. #107×C53 | C22 | semidirect |
| 42. #106×C53 | C22 | semidirect |
| 160. #428 | D53 | semidirect |
| 164. C53 | #3093 | semidirect |
| 187. #107 | C2×D53 | semidirect |
| 189. #106 | C2×D53 | semidirect |