Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
460 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 460 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 |
|---|---|---|
| 3. #16810952 | C2 | direct (N × H) |
| 4. C2×#13133149 | C2 | semidirect |
| 5. C2×#13133148 | C2 | semidirect |
| 6. C2×#13133141 | C2 | semidirect |
| 8. C2×#103×C53 | C2 | semidirect |
| 21. #13133149 | C22 | semidirect |
| 22. #13133148 | C22 | semidirect |
| 23. #13133141 | C22 | semidirect |
| 28. #103×C53 | C22 | semidirect |
| 104. C2×C53 | #483 | semidirect |
| 115. C2×#103 | D53 | semidirect |
| 117. C53 | C2×#483 | semidirect |
| 136. #103 | C2×D53 | semidirect |
| 213. C2 | #16810952 | direct (N × H) |