Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 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 |
|---|---|---|
| 1. #16811180 | C2 | semidirect |
| 3. #16810954 | C2 | semidirect |
| 4. #16810914 | C2 | semidirect |
| 5. #16810829 | C2 | semidirect |
| 7. C4×#11719913 | C2 | semidirect |
| 8. C53×#431 | C2 | semidirect |
| 12. #13133217 | C22 | semidirect |
| 13. #13133217 | C22 | semidirect |
| 18. C4×Dic106 | C22 | semidirect |
| 26. #13133149 | C22 | semidirect |
| 27. #13133142 | C22 | semidirect |
| 30. C4⋊C8×C53 | C22 | semidirect |
| 32. C4×C8×C53 | C22 | semidirect |
| 71. C2×C4×C53 | SD16 | semidirect |
| 120. #431 | D53 | semidirect |
| 121. C53 | #3101 | semidirect |
| 141. C4⋊C8 | C2×D53 | semidirect |
| 145. C4×C8 | C2×D53 | semidirect |
| 195. C2×C4 | #11719913 | semidirect |