Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 145 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×#13133250 | C2 | semidirect |
| 3. #16811194 | C2 | semidirect |
| 4. #16810808 | C2 | semidirect |
| 5. #16810803 | C2 | semidirect |
| 6. #16810639 | C2 | semidirect |
| 7. C53×#413 | C2 | semidirect |
| 16. C22×Dic106 | C22 | semidirect |
| 18. #13133250 | C22 | semidirect |
| 21. #13133215 | C22 | semidirect |
| 22. #13133204 | C22 | semidirect |
| 25. #13133176 | C22 | semidirect |
| 26. #13133143 | C22 | semidirect |
| 28. C2×M16×C53 | C22 | semidirect |
| 29. #101×C53 | C22 | semidirect |
| 30. #100×C53 | C22 | semidirect |
| 136. #413 | D53 | semidirect |
| 137. C53 | #3022 | semidirect |
| 152. C2×M16 | C2×D53 | semidirect |
| 159. #101 | C2×D53 | semidirect |
| 160. #100 | C2×D53 | semidirect |