Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
454 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 129 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. #16811157 | C2 | semidirect |
| 2. C2×C4×D212 | C2 | semidirect |
| 3. #16810959 | C2 | semidirect |
| 4. #16810942 | C2 | semidirect |
| 5. #16810924 | C2 | semidirect |
| 6. #16810839 | C2 | semidirect |
| 7. #16810776 | C2 | semidirect |
| 9. C4×#11719913 | C2 | semidirect |
| 10. C4×D424 | C2 | semidirect |
| 11. C53×#431 | C2 | semidirect |
| 17. #13133209 | C22 | semidirect |
| 18. #13133205 | C22 | semidirect |
| 22. C4×Dic106 | C22 | semidirect |
| 27. C4×D212 | C22 | semidirect |
| 32. #13133151 | C22 | semidirect |
| 33. #13133149 | C22 | semidirect |
| 34. #13133142 | C22 | semidirect |
| 37. #13133139 | C22 | semidirect |
| 39. C4⋊C8×C53 | C22 | semidirect |
| 42. C4×C8×C53 | C22 | semidirect |
| 151. #431 | D53 | semidirect |
| 152. C53 | #3105 | semidirect |
| 176. C4⋊C8 | C2×D53 | semidirect |
| 183. C4×C8 | C2×D53 | semidirect |