Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
266 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 61 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×#13133158 | C2 | semidirect |
| 2. #16810859 | C2 | semidirect |
| 3. #16810424 | C2 | semidirect |
| 4. C22⋊#11719908 | C2 | semidirect |
| 5. C22×D8×C53 | C2 | semidirect |
| 6. C2×D424 | C22 | semidirect |
| 9. C2×#11719908 | C22 | semidirect |
| 10. #13133151 | C22 | semidirect |
| 27. D8×C53 | D4 | semidirect |
| 60. C22×C53 | D16 | semidirect |
| 76. C22×D8 | D53 | semidirect |
| 81. C53 | #2184 | semidirect |
| 104. D8 | C22⋊D53 | semidirect |
| 139. C22 | #13133158 | semidirect |