Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
266 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 57 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. C22×D424 | C2 | semidirect |
| 2. C2×#13133158 | C2 | semidirect |
| 3. #16810423 | C2 | semidirect |
| 4. C22⋊#11719908 | C2 | semidirect |
| 5. C53×#466 | C2 | semidirect |
| 11. C2×#11719908 | C22 | semidirect |
| 12. C2×D8×C53 | C22 | semidirect |
| 15. #107×C53 | C22 | semidirect |
| 33. D424 | D4 | semidirect |
| 59. C22×C53 | D16 | semidirect |
| 78. #466 | D53 | semidirect |
| 81. C53 | #2184 | semidirect |
| 86. C2×D8 | C2×D53 | semidirect |
| 91. #107 | C2×D53 | semidirect |
| 139. C22 | #13133158 | semidirect |