Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 4. #16810384 | C2 | semidirect |
| 5. #16810382 | C2 | semidirect |
| 6. #16810379 | C2 | semidirect |
| 7. C53×H(3,ℤ/4) | C2 | semidirect |
| 14. #13133174 | C4 | semidirect |
| 16. C42×D53 | C4 | semidirect |
| 109. H(3,ℤ/4) | D53 | semidirect |
| 110. C53 | #1827 | semidirect |