Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#13133237 | C2 | semidirect |
| 2. #16811278 | C2 | semidirect |
| 3. #16811002 | C2 | semidirect |
| 4. #16810862 | C2 | semidirect |
| 5. #16810828 | C2 | semidirect |
| 6. #16810825 | C2 | semidirect |
| 7. #16810785 | C2 | semidirect |
| 8. #16810783 | C2 | semidirect |
| 9. C4×#11719922 | C2 | semidirect |
| 10. D4×#88322 | C2 | semidirect |
| 11. C53×#547 | C2 | semidirect |
| 72. #11719922 | D4 | semidirect |
| 127. C4×C53 | #135 | semidirect |
| 141. #547 | D53 | semidirect |
| 150. C53 | #3283 | semidirect |
| 268. C4 | #13133237 | semidirect |