Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
404 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 129 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×#13133141 | C2 | semidirect |
| 4. #16810385 | C2 | semidirect |
| 16. C22⋊Q8×C53 | C4 | semidirect |
| 24. C2×Q8×C53 | C2×C4 | semidirect |
| 39. C4⋊C4×C53 | C2×C4 | semidirect |
| 83. C22×C53 | #103 | semidirect |
| 111. C53 | #1872 | semidirect |
| 117. C22⋊Q8 | Dic53 | semidirect |
| 130. C2×Q8 | C2×Dic53 | semidirect |
| 151. C4⋊C4 | C2×Dic53 | semidirect |
| 189. C22 | #13133141 | semidirect |