Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 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 |
|---|---|---|
| 1. C2×#13133245 | C2 | semidirect |
| 2. C2×#13133242 | C2 | semidirect |
| 3. #16811169 | C2 | semidirect |
| 4. C2×#13133179 | C2 | semidirect |
| 5. #16810841 | C2 | semidirect |
| 6. #16810837 | C2 | semidirect |
| 7. #16810827 | C2 | semidirect |
| 8. #16810817 | C2 | semidirect |
| 9. #16810646 | C2 | semidirect |
| 10. #16810622 | C2 | semidirect |
| 11. C53×#417 | C2 | semidirect |
| 22. #13133215 | C22 | semidirect |
| 23. #13133213 | C22 | semidirect |
| 24. #13133206 | C22 | semidirect |
| 25. #13133204 | C22 | semidirect |
| 36. #13133146 | C22 | semidirect |
| 37. #13133146 | C22 | semidirect |
| 38. #13133140 | C22 | semidirect |
| 39. #13133137 | C22 | semidirect |
| 43. #103×C53 | C22 | semidirect |
| 44. #102×C53 | C22 | semidirect |
| 63. C2×D212 | D4 | semidirect |
| 158. Dic53 | AGL(1,ℤ/8) | semidirect |
| 177. #417 | D53 | semidirect |
| 178. C53 | #3036 | semidirect |
| 209. #103 | C2×D53 | semidirect |
| 211. #102 | C2×D53 | semidirect |