Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
144 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 144 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×#13133162 | C2 | semidirect |
| 2. #16810898 | C2 | semidirect |
| 4. #16810453 | C2 | semidirect |
| 5. #16810440 | C2 | semidirect |
| 6. #16810437 | C2 | semidirect |
| 7. C53×#504 | C2 | semidirect |
| 73. #504 | D53 | semidirect |
| 79. C53 | #2223 | semidirect |