Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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. #16810910 | C2 | semidirect |
| 4. #16810900 | C2 | semidirect |
| 5. #16810666 | C2 | semidirect |
| 6. #16810647 | C2 | semidirect |
| 8. C53×#533 | C2 | semidirect |
| 18. #13133150 | C22 | semidirect |
| 19. #13133148 | C22 | semidirect |
| 20. C4⋊#88322 | C22 | semidirect |
| 21. C4⋊#88322 | C22 | semidirect |
| 24. C4⋊Q8×C53 | C22 | semidirect |
| 25. C4⋊Q8×C53 | C22 | semidirect |
| 26. #125×C53 | C22 | semidirect |
| 42. C2×D212 | Q8 | semidirect |
| 116. #533 | D53 | semidirect |
| 124. C53 | #3077 | semidirect |
| 128. C4⋊Q8 | C2×D53 | semidirect |
| 129. C4⋊Q8 | C2×D53 | semidirect |
| 130. #125 | C2×D53 | semidirect |