Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
390 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×Q8×Dic53 | C2 | semidirect |
| 3. #16810951 | C2 | semidirect |
| 5. #16810932 | C2 | semidirect |
| 6. #16810847 | C2 | semidirect |
| 8. Q16×Dic53 | C2 | semidirect |
| 9. #16810708 | C2 | semidirect |
| 10. #16810673 | C2 | semidirect |
| 11. C53×#451 | C2 | semidirect |
| 138. #451 | D53 | semidirect |
| 143. C53 | #3108 | semidirect |