Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
186 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 186 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×D848 | C2 | semidirect |
| 2. C2×#13133158 | C2 | semidirect |
| 3. #16810998 | C2 | semidirect |
| 4. #16810705 | C2 | semidirect |
| 5. #16810441 | C2 | semidirect |
| 6. #16810423 | C2 | semidirect |
| 7. C53×#357 | C2 | semidirect |
| 38. D424 | D4 | semidirect |
| 74. Dic53 | D16 | semidirect |
| 88. #357 | D53 | semidirect |
| 89. C53 | #2206 | semidirect |