Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
270 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 83 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×#13133153 | C2 | semidirect |
| 3. #16810649 | C2 | semidirect |
| 6. #16810383 | C2 | semidirect |
| 7. C53×#336 | C2 | semidirect |
| 20. #13133142 | C4 | semidirect |
| 21. #13133142 | C4 | semidirect |
| 22. #13133139 | C4 | semidirect |
| 23. #13133139 | C4 | semidirect |
| 116. #336 | D53 | semidirect |
| 117. C53 | #1866 | semidirect |