Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
806 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 169 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. C2×#13133191 | C2 | semidirect |
| 3. #16810768 | C2 | semidirect |
| 4. #16810762 | C2 | semidirect |
| 5. #16810757 | C2 | semidirect |
| 6. #16810624 | C2 | semidirect |
| 7. #16810587 | C2 | semidirect |
| 8. C22×#41×C53 | C2 | semidirect |
| 9. C22×D212 | C22 | semidirect |
| 12. C2×#11719924 | C22 | semidirect |
| 13. C2×#11719922 | C22 | semidirect |
| 14. C2×#11719917 | C22 | semidirect |
| 18. #13133191 | C22 | semidirect |
| 19. C2×C4⋊Dic53 | C22 | semidirect |
| 21. #13133141 | C22 | semidirect |
| 22. #13133138 | C22 | semidirect |
| 23. C22⋊#88322 | C22 | semidirect |
| 24. C22⋊#88322 | C22 | semidirect |
| 29. C2×#41×C53 | C22 | semidirect |
| 30. C22×Q8×C53 | C22 | semidirect |
| 32. C22×D4×C53 | C22 | semidirect |
| 43. #41×C53 | D4 | semidirect |
| 95. Q8×C53 | C2×D4 | semidirect |
| 100. D4×C53 | C2×D4 | semidirect |
| 135. C22×C53 | AGL(1,ℤ/8) | semidirect |
| 156. C22×#41 | D53 | semidirect |
| 164. C53 | #3006 | semidirect |
| 169. C2×#41 | C2×D53 | semidirect |
| 170. C22×Q8 | C2×D53 | semidirect |
| 174. C22×D4 | C2×D53 | semidirect |
| 199. #41 | C22⋊D53 | semidirect |
| 251. Q8 | C2×C22⋊D53 | semidirect |
| 260. D4 | C2×C22⋊D53 | semidirect |
| 295. C22 | #13133242 | semidirect |