Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 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×#13133245 | C2 | semidirect |
| 2. C22×D424 | C2 | semidirect |
| 3. C2×#13133223 | C2 | semidirect |
| 4. #16810894 | C2 | direct (N × H) |
| 5. C2×#13133133 | C2 | semidirect |
| 6. C2×#108×C53 | C2 | semidirect |
| 10. #13133245 | C22 | semidirect |
| 16. C2×D424 | C22 | semidirect |
| 18. #13133223 | C22 | semidirect |
| 22. #13133133 | C22 | semidirect |
| 25. #108×C53 | C22 | semidirect |
| 105. C2×C53 | #472 | semidirect |
| 113. C2×#108 | D53 | semidirect |
| 115. C53 | C2×#472 | semidirect |
| 133. #108 | C2×D53 | semidirect |
| 215. C2 | #16810894 | direct (N × H) |