Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
| 2. C2×#13133204 | C2 | semidirect |
| 3. #16810801 | C2 | direct (N × H) |
| 4. C2×#13133144 | C2 | semidirect |
| 5. C2×#13133134 | C2 | semidirect |
| 7. C22×Dic106 | C22 | semidirect |
| 9. #13133247 | C22 | semidirect |
| 12. C2×#11719917 | C22 | semidirect |
| 14. #13133204 | C22 | semidirect |
| 16. C2×C4×Dic53 | C22 | semidirect |
| 17. #13133144 | C22 | semidirect |
| 18. #13133134 | C22 | semidirect |
| 55. C2×Dic106 | C23 | semidirect |
| 60. C4×Dic53 | C23 | semidirect |
| 62. #11719917 | C23 | semidirect |
| 118. C2×C53 | #455 | semidirect |
| 126. C53 | C2×#455 | semidirect |
| 237. C2 | #16810801 | direct (N × H) |