Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13133242 | C2 | semidirect |
| 2. C2×#13133224 | C2 | semidirect |
| 3. #16811187 | C2 | semidirect |
| 4. #16810874 | C2 | semidirect |
| 5. #16810871 | C2 | semidirect |
| 6. #16810857 | C2 | semidirect |
| 7. #16810854 | C2 | semidirect |
| 8. #16810663 | C2 | semidirect |
| 9. #16810619 | C2 | semidirect |
| 10. C2×#13133137 | C2 | semidirect |
| 11. C53×#537 | C2 | semidirect |
| 18. C2×#11719917 | C22 | semidirect |
| 20. C22×#88322 | C22 | semidirect |
| 27. #13133150 | C22 | semidirect |
| 28. #13133148 | C22 | semidirect |
| 29. #13133141 | C22 | semidirect |
| 30. #13133141 | C22 | semidirect |
| 31. #13133138 | C22 | semidirect |
| 32. #13133138 | C22 | semidirect |
| 38. C22⋊Q8×C53 | C22 | semidirect |
| 41. #121×C53 | C22 | semidirect |
| 79. #11719917 | D4 | semidirect |
| 154. #537 | D53 | semidirect |
| 163. C53 | #3062 | semidirect |
| 178. C22⋊Q8 | C2×D53 | semidirect |
| 183. #121 | C2×D53 | semidirect |