Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
408 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#13133131 | C2 | semidirect |
| 3. #16810483 | C2 | semidirect |
| 4. C4×C22⋊C4×C53 | C2 | semidirect |
| 5. C22×D212 | C4 | semidirect |
| 12. C2×C4⋊Dic53 | C4 | semidirect |
| 14. C2×#11719921 | C4 | semidirect |
| 41. C22⋊C4×C53 | D4 | semidirect |
| 104. C4×C53 | #99 | semidirect |
| 119. C4×C22⋊C4 | D53 | semidirect |
| 120. C53 | #1964 | semidirect |
| 163. C22⋊C4 | D212 | semidirect |
| 222. C4 | #13133131 | semidirect |