Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
546 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 546 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. C22×#11719923 | C2 | semidirect |
| 2. D4×Dic106 | C2 | semidirect |
| 3. #16810995 | C2 | semidirect |
| 4. #16810850 | C2 | semidirect |
| 5. #16810828 | C2 | semidirect |
| 6. #16810820 | C2 | semidirect |
| 7. #16810774 | C2 | semidirect |
| 8. #16810761 | C2 | semidirect |
| 9. C4×#11719923 | C2 | semidirect |
| 10. D4×#88322 | C2 | semidirect |
| 12. C22×Dic106 | C22 | semidirect |
| 16. C2×#11719923 | C22 | semidirect |
| 17. C2×#11719923 | C22 | semidirect |
| 18. C2×#11719923 | C22 | semidirect |
| 19. C22×#88322 | C22 | semidirect |
| 20. #13133217 | C22 | semidirect |
| 22. #13133196 | C22 | semidirect |
| 24. C4×Dic106 | C22 | semidirect |
| 26. #13133148 | C22 | semidirect |
| 27. C4⋊#88322 | C22 | semidirect |
| 28. #13133140 | C22 | semidirect |
| 29. #13133140 | C22 | semidirect |
| 31. #13133138 | C22 | semidirect |
| 32. C22⋊#88322 | C22 | semidirect |
| 33. C4×#88322 | C22 | semidirect |
| 72. #11719923 | D4 | direct (N × H) |
| 96. D4×C53 | SD16 | semidirect |
| 114. Dic106 | C2×D4 | semidirect |
| 117. #88322 | C2×D4 | semidirect |
| 127. C22×C53 | C2×SD16 | semidirect |
| 132. C4×C53 | C2×SD16 | semidirect |
| 156. C53 | D4×SD16 | semidirect |
| 246. D4 | #11719923 | direct (N × H) |
| 272. C22 | C2×#11719923 | semidirect |
| 280. C4 | C2×#11719923 | semidirect |