Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
784 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13133242 | C2 | semidirect |
| 2. C22×#11719922 | C2 | semidirect |
| 3. #16811187 | C2 | semidirect |
| 4. #16810768 | C2 | semidirect |
| 5. #16810757 | C2 | semidirect |
| 6. #16810628 | C2 | semidirect |
| 7. #16810619 | C2 | semidirect |
| 8. #16810590 | C2 | semidirect |
| 9. C2×H(5,𝔽2)×C53 | C2 | semidirect |
| 10. C22×D212 | C22 | semidirect |
| 12. C2×#11719924 | C22 | semidirect |
| 14. C2×#11719922 | C22 | semidirect |
| 15. C2×#11719922 | C22 | semidirect |
| 16. C2×#11719917 | C22 | semidirect |
| 17. C22×#88322 | C22 | semidirect |
| 20. #13133191 | C22 | semidirect |
| 22. #13133176 | C22 | semidirect |
| 23. #13133141 | C22 | semidirect |
| 24. #13133138 | C22 | semidirect |
| 25. #13133138 | C22 | semidirect |
| 26. C22⋊#88322 | C22 | semidirect |
| 32. C2×#41×C53 | C22 | semidirect |
| 36. C22×D4×C53 | C22 | semidirect |
| 46. #41×C53 | D4 | semidirect |
| 60. C2×D4×C53 | D4 | semidirect |
| 152. C2×H(5,𝔽2) | D53 | semidirect |
| 161. C53 | #3008 | semidirect |
| 167. C2×#41 | C2×D53 | semidirect |
| 172. C22×D4 | C2×D53 | semidirect |
| 198. #41 | C22⋊D53 | semidirect |
| 217. C2×D4 | C22⋊D53 | semidirect |