Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
160 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 49 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×#13133156 | C2 | semidirect |
| 2. #16810861 | C2 | semidirect |
| 4. #16810449 | C2 | semidirect |
| 5. #16810427 | C2 | semidirect |
| 6. #16810424 | C2 | semidirect |
| 7. C2×SD32×C53 | C2 | semidirect |
| 38. C16×C53 | D4 | semidirect |
| 76. C2×SD32 | D53 | semidirect |
| 83. C53 | #2220 | semidirect |
| 115. C16 | C22⋊D53 | semidirect |