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 |
|---|---|---|
| 1. #16811180 | C2 | semidirect |
| 3. #16810965 | C2 | semidirect |
| 4. #16810909 | C2 | semidirect |
| 5. #16810904 | C2 | semidirect |
| 6. #16810834 | C2 | semidirect |
| 7. #16810829 | C2 | semidirect |
| 9. C4×Dic212 | C2 | semidirect |
| 10. C4×#11719913 | C2 | semidirect |
| 11. C53×#431 | C2 | semidirect |
| 147. #431 | D53 | semidirect |
| 148. C53 | #3107 | semidirect |