Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#11719913 | C2 | semidirect |
| 2. #16811194 | C2 | semidirect |
| 4. #16810869 | C2 | semidirect |
| 5. #16810852 | C2 | semidirect |
| 6. #16810661 | C2 | semidirect |
| 7. #16810633 | C2 | semidirect |
| 8. #16810629 | C2 | semidirect |
| 9. C2×#131×C53 | C2 | semidirect |
| 20. #13133196 | C22 | semidirect |
| 25. #13133151 | C22 | semidirect |
| 26. #13133149 | C22 | semidirect |
| 27. #13133142 | C22 | semidirect |
| 32. C2×M16×C53 | C22 | semidirect |
| 34. C22×C8×C53 | C22 | semidirect |
| 56. C2×C8×C53 | D4 | semidirect |
| 122. C2×#131 | D53 | semidirect |
| 130. C53 | #3057 | semidirect |
| 139. C2×M16 | C2×D53 | semidirect |
| 141. C22×C8 | C2×D53 | semidirect |
| 179. C2×C8 | C22⋊D53 | semidirect |