Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
144 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 45 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. #16811039 | C2 | semidirect |
| 2. #16810895 | C2 | semidirect |
| 4. #16810453 | C2 | semidirect |
| 5. #16810439 | C2 | semidirect |
| 6. #16810436 | C2 | semidirect |
| 7. C2×SD32×C53 | C2 | semidirect |
| 72. C2×SD32 | D53 | semidirect |
| 79. C53 | #2223 | semidirect |