Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 1. C2×#13133247 | C2 | semidirect |
| 2. C2×#13133204 | C2 | semidirect |
| 3. #41×Dic53 | C2 | semidirect |
| 4. #16810843 | C2 | semidirect |
| 5. #16810836 | C2 | semidirect |
| 6. #16810646 | C2 | semidirect |
| 7. #16810633 | C2 | semidirect |
| 8. #16810628 | C2 | semidirect |
| 12. C2×#11719925 | C22 | semidirect |
| 13. C2×#11719923 | C22 | semidirect |
| 18. Q8×Dic53 | C22 | semidirect |
| 20. D4×Dic53 | C22 | semidirect |
| 26. #13133146 | C22 | semidirect |
| 27. #13133142 | C22 | semidirect |
| 135. C53 | #3040 | semidirect |