Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#13133265 | C2 | semidirect |
| 2. C2×#13133243 | C2 | semidirect |
| 3. #16810795 | C2 | direct (N × H) |
| 4. C2×#13133145 | C2 | semidirect |
| 5. C2×#13133136 | C2 | semidirect |
| 6. C2×#124×C53 | C2 | semidirect |
| 9. #13133265 | C22 | semidirect |
| 15. #13133243 | C22 | semidirect |
| 19. #13133145 | C22 | semidirect |
| 20. #13133136 | C22 | semidirect |
| 24. #124×C53 | C22 | semidirect |
| 115. C2×C53 | #454 | semidirect |
| 120. C2×#124 | D53 | semidirect |
| 124. C53 | C2×#454 | semidirect |
| 140. #124 | C2×D53 | semidirect |
| 233. C2 | #16810795 | direct (N × H) |