Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 3. #16810633 | C2 | semidirect |
| 4. #16810631 | C2 | semidirect |
| 6. #16810379 | C2 | semidirect |
| 7. C53×H(3,ℤ/4) | C2 | semidirect |
| 14. #13133217 | C4 | semidirect |
| 15. #13133205 | C4 | semidirect |
| 116. H(3,ℤ/4) | D53 | semidirect |
| 117. C53 | #1909 | semidirect |