Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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. C22×#11719924 | C2 | semidirect |
| 3. #16811097 | C2 | semidirect |
| 4. #16810835 | C2 | semidirect |
| 5. #16810825 | C2 | semidirect |
| 6. #16810650 | C2 | semidirect |
| 7. #16810632 | C2 | semidirect |
| 8. #16810619 | C2 | semidirect |
| 9. C53×#536 | C2 | semidirect |
| 22. C4⋊#88322 | C22 | semidirect |
| 23. #13133141 | C22 | semidirect |
| 24. #13133141 | C22 | semidirect |
| 25. #13133138 | C22 | semidirect |
| 28. C4⋊Q8×C53 | C22 | semidirect |
| 29. #124×C53 | C22 | semidirect |
| 119. #536 | D53 | semidirect |
| 126. C53 | #3042 | semidirect |
| 137. C4⋊Q8 | C2×D53 | semidirect |
| 138. #124 | C2×D53 | semidirect |