Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #16810920 | C2 | semidirect |
| 3. #16810920 | C2 | semidirect |
| 4. #16810910 | C2 | semidirect |
| 5. #16810900 | C2 | semidirect |
| 6. #16810663 | C2 | semidirect |
| 7. #16810659 | C2 | semidirect |
| 8. #16810650 | C2 | semidirect |
| 11. C53×#544 | C2 | 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 |
| 34. C4⋊Q8×C53 | C22 | semidirect |
| 36. #125×C53 | C22 | semidirect |
| 47. C2×D212 | Q8 | semidirect |
| 125. #544 | D53 | semidirect |
| 136. C53 | #3081 | semidirect |
| 141. C4⋊Q8 | C2×D53 | semidirect |
| 143. #125 | C2×D53 | semidirect |