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×#13133247 | C2 | semidirect |
| 3. C2×#13133205 | C2 | semidirect |
| 4. #16810845 | C2 | semidirect |
| 5. #16810838 | C2 | semidirect |
| 6. #16810647 | C2 | semidirect |
| 7. #16810631 | C2 | semidirect |
| 8. #16810627 | C2 | semidirect |
| 9. C4×#41×C53 | C2 | semidirect |
| 14. C2×#11719925 | C22 | semidirect |
| 15. C2×#11719923 | C22 | semidirect |
| 24. C4⋊#88322 | C22 | semidirect |
| 25. #13133140 | C22 | semidirect |
| 28. C4×Q8×C53 | C22 | semidirect |
| 30. C4×D4×C53 | C22 | semidirect |
| 129. C4×#41 | D53 | semidirect |
| 135. C53 | #3040 | semidirect |
| 150. C4×Q8 | C2×D53 | semidirect |
| 152. C4×D4 | C2×D53 | semidirect |