Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
174 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 2. D8×Dic53 | C2 | semidirect |
| 3. #16810705 | C2 | semidirect |
| 4. #16810448 | C2 | semidirect |
| 5. #16810425 | C2 | semidirect |
| 6. C16×Dic53 | C2 | semidirect |
| 7. C53×#357 | C2 | semidirect |
| 11. #13133158 | C4 | semidirect |
| 25. D8×C53 | C2×C4 | semidirect |
| 34. D424 | C2×C4 | semidirect |
| 36. #11719908 | C2×C4 | semidirect |
| 65. Dic53 | D16 | semidirect |
| 77. #357 | D53 | semidirect |
| 79. C53 | C4×D16 | semidirect |
| 99. D8 | C4×D53 | semidirect |