Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16810973 | C2 | semidirect |
| 3. #16810961 | C2 | semidirect |
| 4. #16810918 | C2 | semidirect |
| 5. #16810871 | C2 | semidirect |
| 6. #16810825 | C2 | semidirect |
| 7. #16810762 | C2 | semidirect |
| 8. C4×#11719924 | C2 | semidirect |
| 9. #16810701 | C2 | semidirect |
| 10. #16810632 | C2 | semidirect |
| 11. D4×Q8×C53 | C2 | semidirect |
| 128. D4×Q8 | D53 | semidirect |
| 138. C53 | #3329 | semidirect |