Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
456 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 125 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×#13133137 | C2 | semidirect |
| 3. C2×C22⋊#88322 | C2 | semidirect |
| 4. #16810385 | C2 | semidirect |
| 5. C22×C4⋊C4×C53 | C2 | semidirect |
| 10. #13133191 | C4 | semidirect |
| 39. C2×D212 | C2×C4 | semidirect |
| 42. C4⋊C4×C53 | D4 | semidirect |
| 45. C4⋊Dic53 | C2×C4 | semidirect |
| 90. C22×C53 | #102 | semidirect |
| 121. C22×C4⋊C4 | D53 | semidirect |
| 125. C53 | #1874 | semidirect |
| 167. C4⋊C4 | C22⋊D53 | semidirect |
| 217. C22 | #13133137 | semidirect |