Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
142 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 142 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 |
|---|---|---|
| 2. #16810661 | C2 | semidirect |
| 3. #16810451 | C2 | semidirect |
| 4. #16810449 | C2 | semidirect |
| 5. #16810425 | C2 | semidirect |
| 6. #16810425 | C2 | semidirect |
| 7. C53×C22⋊C16 | C2 | semidirect |
| 76. C22⋊C16 | D53 | semidirect |
| 77. C53 | #2234 | semidirect |