Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
320 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 320 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. #16810646 | C2 | semidirect |
| 3. C2×#13133145 | C2 | semidirect |
| 4. C2×#13133144 | C2 | semidirect |
| 5. C2×#13133143 | C2 | semidirect |
| 6. #16810469 | C2 | semidirect |
| 7. C2×#104×C53 | C2 | semidirect |
| 10. #13133215 | C4 | semidirect |
| 11. #13133213 | C4 | semidirect |
| 12. #13133206 | C4 | semidirect |
| 13. #13133204 | C4 | semidirect |
| 52. C42×C53 | D4 | semidirect |
| 60. C4×Dic53 | D4 | semidirect |
| 131. C2×#104 | D53 | semidirect |
| 133. C53 | #1963 | semidirect |
| 189. C42 | C22⋊D53 | semidirect |