Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 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×#13133247 | C2 | semidirect |
| 2. C22×#11719923 | C2 | semidirect |
| 3. C2×#13133224 | C2 | semidirect |
| 4. #16810884 | C2 | direct (N × H) |
| 5. C2×#13133152 | C2 | semidirect |
| 6. C2×#13133135 | C2 | semidirect |
| 7. C2×#13133134 | C2 | semidirect |
| 11. #13133247 | C22 | semidirect |
| 17. C2×#11719923 | C22 | semidirect |
| 19. #13133224 | C22 | semidirect |
| 25. #13133152 | C22 | semidirect |
| 26. #13133135 | C22 | semidirect |
| 27. #13133134 | C22 | semidirect |
| 137. C2×C53 | #471 | semidirect |
| 147. C53 | C2×#471 | semidirect |
| 275. C2 | #16810884 | direct (N × H) |