Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 2. C2×C4⋊C4×D53 | C2 | semidirect |
| 3. #16810938 | C2 | semidirect |
| 4. #16810937 | C2 | semidirect |
| 5. #16810936 | C2 | semidirect |
| 6. #16810935 | C2 | semidirect |
| 7. #16810934 | C2 | semidirect |
| 8. #107×D53 | C2 | semidirect |
| 9. #102×D53 | C2 | semidirect |
| 10. C22⋊C8×D53 | C2 | semidirect |
| 11. C53×#480 | C2 | semidirect |
| 22. C2×C4⋊Dic53 | C22 | semidirect |
| 28. C4⋊C4×D53 | C22 | semidirect |
| 30. #13133151 | C22 | semidirect |
| 31. #13133150 | C22 | semidirect |
| 32. #13133150 | C22 | semidirect |
| 33. #13133139 | C22 | semidirect |
| 34. #13133138 | C22 | semidirect |
| 35. #13133137 | C22 | semidirect |
| 36. C22⋊#88322 | C22 | semidirect |
| 37. #13133129 | C22 | semidirect |
| 39. C2×C4⋊C4×C53 | C22 | semidirect |
| 40. #107×C53 | C22 | semidirect |
| 41. #102×C53 | C22 | semidirect |
| 42. C22⋊C8×C53 | C22 | semidirect |
| 156. D53 | #480 | direct (N × H) |
| 164. #480 | D53 | direct (N × H) |
| 168. C53 | C2×#480 | semidirect |
| 187. C2×C4⋊C4 | C2×D53 | semidirect |
| 192. #107 | C2×D53 | semidirect |
| 196. #102 | C2×D53 | semidirect |
| 199. C22⋊C8 | C2×D53 | semidirect |