Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 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. C2×#13133239 | C2 | semidirect |
| 2. #16811134 | C2 | semidirect |
| 3. #16810881 | C2 | semidirect |
| 4. #16810876 | C2 | semidirect |
| 5. #16810869 | C2 | semidirect |
| 6. #16810661 | C2 | semidirect |
| 7. #16810620 | C2 | semidirect |
| 8. C22×M16×C53 | C2 | semidirect |
| 11. C2×Dic212 | C22 | semidirect |
| 12. C2×#11719913 | C22 | semidirect |
| 13. C2×D424 | C22 | semidirect |
| 20. #13133151 | C22 | semidirect |
| 21. #13133149 | C22 | semidirect |
| 22. #13133142 | C22 | semidirect |
| 23. #13133139 | C22 | semidirect |
| 47. C2×C8×C53 | D4 | semidirect |
| 107. C22×M16 | D53 | semidirect |
| 114. C53 | #3054 | semidirect |
| 156. C2×C8 | C22⋊D53 | semidirect |