Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 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 |
|---|---|---|
| 2. C2×#13133162 | C2 | semidirect |
| 3. #16810864 | C2 | semidirect |
| 4. #16810425 | C2 | semidirect |
| 5. C53×C22⋊C16 | C2 | semidirect |
| 7. C2×Dic212 | C22 | semidirect |
| 13. #13133151 | C22 | semidirect |
| 16. C2×C16×C53 | C22 | semidirect |
| 55. C22×C53 | SD32 | semidirect |
| 76. C22⋊C16 | D53 | semidirect |
| 77. C53 | #2187 | semidirect |
| 86. C2×C16 | C2×D53 | semidirect |
| 131. C22 | #13133162 | semidirect |