Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
398 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 149 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. #16811251 | C2 | semidirect |
| 2. #16810923 | C2 | semidirect |
| 3. #16810923 | C2 | semidirect |
| 4. #16810913 | C2 | semidirect |
| 5. #16810903 | C2 | semidirect |
| 6. #16810666 | C2 | semidirect |
| 7. #16810659 | C2 | semidirect |
| 8. #16810650 | C2 | semidirect |
| 14. #13133217 | C22 | semidirect |
| 16. #13133209 | C22 | semidirect |
| 21. #13133150 | C22 | semidirect |
| 22. #13133150 | C22 | semidirect |
| 23. #13133150 | C22 | semidirect |
| 24. #13133148 | C22 | semidirect |
| 25. #13133148 | C22 | semidirect |
| 26. #13133148 | C22 | semidirect |
| 27. C4⋊#88322 | C22 | semidirect |
| 28. C4⋊#88322 | C22 | semidirect |
| 44. C2×D4×C53 | Q8 | semidirect |
| 136. C53 | #3081 | semidirect |
| 170. C2×D4 | Dic106 | semidirect |