Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
732 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 732 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×#11719924 | C2 | semidirect |
| 3. #16811187 | C2 | semidirect |
| 4. #16810768 | C2 | semidirect |
| 5. #16810762 | C2 | semidirect |
| 6. #16810632 | C2 | semidirect |
| 7. #16810619 | C2 | semidirect |
| 8. #16810590 | C2 | semidirect |
| 9. C2×2−1+4×C53 | C2 | semidirect |
| 23. #13133141 | C22 | semidirect |
| 24. #13133141 | C22 | semidirect |
| 25. #13133138 | C22 | semidirect |
| 26. C22⋊#88322 | C22 | semidirect |
| 33. C2×#41×C53 | C22 | semidirect |
| 36. C22×Q8×C53 | C22 | semidirect |
| 45. #41×C53 | D4 | semidirect |
| 53. C2×Q8×C53 | D4 | semidirect |
| 146. C2×2−1+4 | D53 | semidirect |
| 155. C53 | #3010 | semidirect |
| 162. C2×#41 | C2×D53 | semidirect |
| 165. C22×Q8 | C2×D53 | semidirect |
| 191. #41 | C22⋊D53 | semidirect |
| 199. C2×Q8 | C22⋊D53 | semidirect |