Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#13133176 | C2 | semidirect |
| 3. #16810965 | C2 | semidirect |
| 4. #16810959 | C2 | semidirect |
| 5. #16810954 | C2 | semidirect |
| 6. #16810948 | C2 | semidirect |
| 7. #16810942 | C2 | semidirect |
| 8. #16810937 | C2 | semidirect |
| 9. #16810661 | C2 | semidirect |
| 10. #16810620 | C2 | semidirect |
| 11. C2×C22⋊C8×C53 | C2 | semidirect |
| 30. #13133151 | C22 | semidirect |
| 31. #13133151 | C22 | semidirect |
| 32. #13133149 | C22 | semidirect |
| 33. #13133149 | C22 | semidirect |
| 34. #13133142 | C22 | semidirect |
| 35. #13133142 | C22 | semidirect |
| 36. #13133139 | C22 | semidirect |
| 37. #13133139 | C22 | semidirect |
| 154. C2×C22⋊C8 | D53 | semidirect |
| 155. C53 | #3091 | semidirect |