Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
428 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 141 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. #16810997 | C2 | semidirect |
| 3. #16810973 | C2 | semidirect |
| 4. #16810825 | C2 | semidirect |
| 5. #16810762 | C2 | semidirect |
| 6. #16810676 | C2 | semidirect |
| 7. C2×C4⋊Q8×C53 | C2 | semidirect |
| 65. C2×C4×C53 | SD16 | semidirect |
| 102. C2×C4⋊Q8 | D53 | semidirect |
| 108. C53 | #3206 | semidirect |
| 173. C2×C4 | #11719924 | semidirect |