Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
444 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. #16811097 | C2 | semidirect |
| 3. #16810629 | C2 | semidirect |
| 4. #16810627 | C2 | semidirect |
| 5. C2×#13133133 | C2 | semidirect |
| 6. #16810383 | C2 | semidirect |
| 7. C53×#339 | C2 | semidirect |
| 13. #13133214 | C4 | semidirect |
| 40. C2×D212 | C2×C4 | semidirect |
| 46. C4⋊C4×C53 | D4 | semidirect |
| 50. C42×C53 | C2×C4 | semidirect |
| 53. C4⋊Dic53 | D4 | semidirect |
| 121. #339 | D53 | semidirect |
| 122. C53 | #1887 | semidirect |
| 165. C4⋊C4 | D212 | semidirect |
| 172. C42 | C4×D53 | semidirect |