Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
708 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 708 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×#13133215 | C2 | semidirect |
| 3. #16810806 | C2 | direct (N × H) |
| 4. C2×#13133144 | C2 | semidirect |
| 5. C2×#13133136 | C2 | semidirect |
| 9. #13133247 | C22 | semidirect |
| 14. #13133215 | C22 | semidirect |
| 17. #13133144 | C22 | semidirect |
| 18. #13133136 | C22 | semidirect |
| 111. C2×C53 | #456 | semidirect |
| 119. C53 | C2×#456 | semidirect |
| 223. C2 | #16810806 | direct (N × H) |