Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
450 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23782196 | C2 | semidirect |
| 2. C2×#19104697 | C2 | semidirect |
| 3. #23781995 | C2 | semidirect |
| 4. #23781968 | C2 | semidirect |
| 5. #23781879 | C2 | semidirect |
| 6. #23781818 | C2 | semidirect |
| 8. #23781774 | C2 | semidirect |
| 9. #23781764 | C2 | semidirect |
| 10. #23781719 | C2 | semidirect |
| 11. #480×C163 | C2 | semidirect |
| 17. #19104726 | C22 | semidirect |
| 18. #19104722 | C22 | semidirect |
| 21. #19104700 | C22 | semidirect |
| 23. D4×Dic163 | C22 | semidirect |
| 31. #19104666 | C22 | semidirect |
| 32. Dic163⋊C8 | C22 | semidirect |
| 33. #19104658 | C22 | semidirect |
| 37. #19104645 | C22 | semidirect |
| 40. #107×C163 | C22 | semidirect |
| 41. #102×C163 | C22 | semidirect |
| 140. C163 | #3114 | semidirect |
| 145. #480 | D163 | semidirect |
| 174. #107 | C2×D163 | semidirect |
| 180. #102 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782196 | 2 |
| C2×#19104697 | 2 |
| #23781995 | 2 |
| #23781968 | 2 |
| #23781879 | 2 |
| #23781818 | 2 |
| #23781798 | 2 |
| #23781774 | 2 |
| #23781764 | 2 |
| #23781719 | 2 |
| #480×C163 | 2 |
| #3114 | 163 |