Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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. Q8×D212 | C2 | semidirect |
| 2. #16810982 | C2 | semidirect |
| 3. #16810973 | C2 | semidirect |
| 4. #16810918 | C2 | semidirect |
| 5. #16810903 | C2 | semidirect |
| 7. #16810825 | C2 | semidirect |
| 8. #16810754 | C2 | semidirect |
| 9. #16810721 | C2 | semidirect |
| 11. C53×#556 | C2 | semidirect |
| 123. #556 | D53 | semidirect |
| 134. C53 | #3367 | semidirect |