Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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. #16810971 | C2 | semidirect |
| 3. #16810941 | C2 | semidirect |
| 4. #16810910 | C2 | semidirect |
| 5. #16810854 | C2 | semidirect |
| 6. #16810823 | C2 | semidirect |
| 7. #16810773 | C2 | semidirect |
| 8. C4×#11719924 | C2 | semidirect |
| 9. D4×#88322 | C2 | semidirect |
| 10. C2×#13133137 | C2 | semidirect |
| 11. C53×#554 | C2 | semidirect |
| 15. C2×#11719924 | C22 | semidirect |
| 16. C22×#88322 | C22 | semidirect |
| 22. #13133148 | C22 | semidirect |
| 23. #13133148 | C22 | semidirect |
| 24. C4⋊#88322 | C22 | semidirect |
| 25. #13133141 | C22 | semidirect |
| 28. #13133137 | C22 | semidirect |
| 29. #13133137 | C22 | semidirect |
| 30. #13133137 | C22 | semidirect |
| 31. C22⋊#88322 | C22 | semidirect |
| 32. C4×#88322 | C22 | semidirect |
| 33. C4⋊Q8×C53 | C22 | semidirect |
| 36. C22⋊Q8×C53 | C22 | semidirect |
| 37. C4×Q8×C53 | C22 | semidirect |
| 40. C2×C4⋊C4×C53 | C22 | semidirect |
| 86. D4×C53 | SD16 | semidirect |
| 137. #554 | D53 | semidirect |
| 148. C53 | #3295 | semidirect |
| 154. C4⋊Q8 | C2×D53 | semidirect |
| 158. C22⋊Q8 | C2×D53 | semidirect |
| 162. C4×Q8 | C2×D53 | semidirect |
| 166. C2×C4⋊C4 | C2×D53 | semidirect |
| 231. D4 | #11719924 | semidirect |