Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13133262 | C2 | semidirect |
| 2. C2×#13133243 | C2 | semidirect |
| 3. #16811190 | C2 | semidirect |
| 4. #16810765 | C2 | semidirect |
| 5. #16810755 | C2 | semidirect |
| 6. #16810628 | C2 | semidirect |
| 7. #16810620 | C2 | semidirect |
| 8. #16810589 | C2 | semidirect |
| 9. C22×D8×C53 | C2 | semidirect |
| 15. C2×#11719947 | C22 | semidirect |
| 18. C2×D4×D53 | C22 | semidirect |
| 20. C2×#11719923 | C22 | semidirect |
| 21. C2×#11719922 | C22 | semidirect |
| 22. C2×#11719917 | C22 | semidirect |
| 25. #13133188 | C22 | semidirect |
| 27. #13133176 | C22 | semidirect |
| 28. #13133142 | C22 | semidirect |
| 29. #13133139 | C22 | semidirect |
| 30. #13133138 | C22 | semidirect |
| 31. #13133129 | C22 | semidirect |
| 33. C22×D4×C53 | C22 | semidirect |
| 35. C2×D8×C53 | C22 | semidirect |
| 36. C22×C8×C53 | C22 | semidirect |
| 45. C2×D4×C53 | D4 | semidirect |
| 65. #11719945 | D4 | semidirect |
| 154. C22×D8 | D53 | semidirect |
| 161. C53 | #3008 | semidirect |
| 172. C22×D4 | C2×D53 | semidirect |
| 177. C2×D8 | C2×D53 | semidirect |
| 179. C22×C8 | C2×D53 | semidirect |
| 217. C2×D4 | C22⋊D53 | semidirect |