Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
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×#19104763 | C2 | semidirect |
| 2. C2×#19104760 | C2 | semidirect |
| 3. #23782211 | C2 | semidirect |
| 4. C2×#19104697 | C2 | semidirect |
| 5. #23781883 | C2 | semidirect |
| 6. #23781879 | C2 | semidirect |
| 7. #23781869 | C2 | semidirect |
| 8. #23781859 | C2 | semidirect |
| 9. #23781688 | C2 | semidirect |
| 10. #23781664 | C2 | semidirect |
| 11. #417×C163 | C2 | semidirect |
| 22. #19104733 | C22 | semidirect |
| 23. #19104731 | C22 | semidirect |
| 24. #19104724 | C22 | semidirect |
| 25. #19104722 | C22 | semidirect |
| 36. Dic163⋊C8 | C22 | semidirect |
| 37. Dic163⋊C8 | C22 | semidirect |
| 38. #19104658 | C22 | semidirect |
| 39. #19104655 | C22 | semidirect |
| 43. #103×C163 | C22 | semidirect |
| 44. #102×C163 | C22 | semidirect |
| 51. C2×D652 | D4 | semidirect |
| 158. Dic163 | AGL(1,ℤ/8) | semidirect |
| 166. C163 | #3036 | semidirect |
| 178. #417 | D163 | semidirect |
| 209. #103 | C2×D163 | semidirect |
| 211. #102 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104763 | 2 |
| C2×#19104760 | 2 |
| #23782211 | 2 |
| C2×#19104697 | 2 |
| #23781883 | 2 |
| #23781879 | 2 |
| #23781869 | 2 |
| #23781859 | 2 |
| #23781688 | 2 |
| #23781664 | 2 |
| #417×C163 | 2 |
| #3036 | 163 |