Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
544 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 544 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. C22×#11719923 | C2 | semidirect |
| 2. C22×#11719912 | C2 | semidirect |
| 3. C2×#13133197 | C2 | semidirect |
| 5. #16810868 | C2 | direct (N × H) |
| 6. C2×#13133150 | C2 | semidirect |
| 7. C2×#13133142 | C2 | semidirect |
| 8. C2×#102×C53 | C2 | semidirect |
| 13. C2×#11719923 | C22 | semidirect |
| 15. C2×#11719912 | C22 | semidirect |
| 18. #13133197 | C22 | semidirect |
| 25. #13133150 | C22 | semidirect |
| 26. #13133142 | C22 | semidirect |
| 30. #102×C53 | C22 | semidirect |
| 62. C2×#88322 | D4 | semidirect |
| 97. #88322 | C2×D4 | semidirect |
| 119. C2×C53 | #468 | semidirect |
| 131. C2×#102 | D53 | semidirect |
| 132. C53 | C2×#468 | semidirect |
| 154. #102 | C2×D53 | semidirect |
| 243. C2 | #16810868 | direct (N × H) |