Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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×#11719924 | C2 | semidirect |
| 3. C2×#13133206 | C2 | semidirect |
| 4. C2×#13133179 | C2 | semidirect |
| 5. #16810841 | C2 | direct (N × H) |
| 6. C2×#13133146 | C2 | semidirect |
| 7. C2×#13133137 | C2 | semidirect |
| 8. C2×#103×C53 | C2 | semidirect |
| 13. C2×#11719924 | C22 | semidirect |
| 18. #13133206 | C22 | semidirect |
| 20. #13133179 | C22 | semidirect |
| 25. #13133146 | C22 | semidirect |
| 26. #13133137 | C22 | semidirect |
| 30. #103×C53 | C22 | semidirect |
| 118. C2×C53 | #463 | semidirect |
| 130. C2×#103 | D53 | semidirect |
| 132. C53 | C2×#463 | semidirect |
| 153. #103 | C2×D53 | semidirect |
| 243. C2 | #16810841 | direct (N × H) |