Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
556 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 556 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×#13133244 | C2 | semidirect |
| 2. #16811295 | C2 | semidirect |
| 3. D4×D212 | C2 | semidirect |
| 4. #16811000 | C2 | semidirect |
| 5. #16810877 | C2 | semidirect |
| 6. #16810823 | C2 | semidirect |
| 7. #16810818 | C2 | semidirect |
| 8. #16810771 | C2 | semidirect |
| 9. #16810758 | C2 | semidirect |
| 10. #16810702 | C2 | semidirect |
| 11. C4×SD16×C53 | C2 | semidirect |
| 12. C2×#11719949 | C22 | semidirect |
| 16. C2×#11719924 | C22 | semidirect |
| 17. C2×D424 | C22 | semidirect |
| 18. C2×D424 | C22 | semidirect |
| 20. C2×#11719912 | C22 | semidirect |
| 23. #13133214 | C22 | semidirect |
| 26. #13133192 | C22 | semidirect |
| 31. C4⋊#88322 | C22 | semidirect |
| 32. #13133137 | C22 | semidirect |
| 33. #13133137 | C22 | semidirect |
| 34. #13133129 | C22 | semidirect |
| 36. C4×Q8×C53 | C22 | semidirect |
| 38. #106×C53 | C22 | semidirect |
| 39. #103×C53 | C22 | semidirect |
| 41. C4×C8×C53 | C22 | semidirect |
| 64. SD16×C53 | D4 | semidirect |
| 91. Q8×C53 | C2×D4 | semidirect |
| 119. C8×C53 | C2×D4 | semidirect |
| 139. C4×C53 | AGL(1,ℤ/8) | semidirect |
| 160. C4×SD16 | D53 | semidirect |
| 162. C53 | #3274 | semidirect |
| 181. C4×Q8 | C2×D53 | semidirect |
| 185. #106 | C2×D53 | semidirect |
| 187. #103 | C2×D53 | semidirect |
| 192. C4×C8 | C2×D53 | semidirect |
| 216. SD16 | D212 | semidirect |
| 242. Q8 | C2×D212 | semidirect |
| 271. C8 | C2×D212 | semidirect |
| 291. C4 | #13133244 | semidirect |