Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
440 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 153 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. #16811180 | C2 | semidirect |
| 2. #16810923 | C2 | semidirect |
| 3. #16810913 | C2 | semidirect |
| 4. #16810903 | C2 | semidirect |
| 5. #16810663 | C2 | semidirect |
| 6. #16810647 | C2 | semidirect |
| 10. #13133217 | C22 | semidirect |
| 11. #13133217 | C22 | semidirect |
| 12. #13133209 | C22 | semidirect |
| 18. #13133150 | C22 | semidirect |
| 19. #13133148 | C22 | semidirect |
| 20. C4⋊#88322 | C22 | semidirect |
| 21. C4⋊#88322 | C22 | semidirect |
| 36. C2×D4×C53 | Q8 | semidirect |
| 124. C53 | #3077 | semidirect |
| 154. C2×D4 | Dic106 | semidirect |