Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 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. #16810965 | C2 | direct (N × H) |
| 4. C2×#13133151 | C2 | semidirect |
| 5. C2×#13133149 | C2 | semidirect |
| 6. C2×#13133142 | C2 | semidirect |
| 7. C2×#13133142 | C2 | semidirect |
| 21. #13133151 | C22 | semidirect |
| 22. #13133149 | C22 | semidirect |
| 23. #13133142 | C22 | semidirect |
| 24. #13133142 | C22 | semidirect |
| 103. C2×C53 | #485 | semidirect |
| 115. C53 | C2×#485 | semidirect |
| 209. C2 | #16810965 | direct (N × H) |