Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
616 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 173 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×#11719922 | C2 | semidirect |
| 2. C23×#88322 | C2 | semidirect |
| 3. C2×#13133191 | C2 | semidirect |
| 4. #16810857 | C2 | direct (N × H) |
| 5. C2×#13133150 | C2 | semidirect |
| 6. C2×#13133138 | C2 | semidirect |
| 7. C2×#13133137 | C2 | semidirect |
| 8. C2×#121×C53 | C2 | semidirect |
| 12. C2×#11719922 | C22 | semidirect |
| 16. C22×#88322 | C22 | semidirect |
| 18. #13133191 | C22 | semidirect |
| 21. #13133150 | C22 | semidirect |
| 22. #13133138 | C22 | semidirect |
| 23. #13133137 | C22 | semidirect |
| 28. #121×C53 | C22 | semidirect |
| 63. C2×#88322 | D4 | semidirect |
| 72. C23×C53 | D8 | semidirect |
| 101. #88322 | C2×D4 | semidirect |
| 111. C22×C53 | C2×D8 | semidirect |
| 127. C2×C53 | #466 | semidirect |
| 135. C2×#121 | D53 | semidirect |
| 140. C53 | C2×#466 | semidirect |
| 155. #121 | C2×D53 | semidirect |
| 208. C23 | #11719922 | semidirect |
| 247. C22 | C2×#11719922 | semidirect |
| 259. C2 | #16810857 | direct (N × H) |