Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
390 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 390 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. #16810961 | C2 | semidirect |
| 3. #16810905 | C2 | semidirect |
| 4. #16810900 | C2 | semidirect |
| 5. #16810830 | C2 | semidirect |
| 6. #16810825 | C2 | semidirect |
| 8. C4×#11719925 | C2 | semidirect |
| 9. C4×#11719924 | C2 | semidirect |
| 10. #16810676 | C2 | semidirect |
| 11. C53×#533 | C2 | semidirect |
| 137. #533 | D53 | semidirect |
| 148. C53 | #3107 | semidirect |