Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23782296 | C2 | semidirect |
| 3. #23782028 | C2 | semidirect |
| 4. #23782023 | C2 | semidirect |
| 5. #23782018 | C2 | semidirect |
| 6. #23782010 | C2 | semidirect |
| 7. #23781670 | C2 | semidirect |
| 8. #23781664 | C2 | semidirect |
| 9. #23781662 | C2 | semidirect |
| 10. #23781620 | C2 | semidirect |
| 11. C2×#102×C163 | C2 | semidirect |
| 15. #19104734 | C22 | semidirect |
| 18. #19104726 | C22 | semidirect |
| 26. #19104660 | C22 | semidirect |
| 27. #19104660 | C22 | semidirect |
| 28. #19104658 | C22 | semidirect |
| 29. #19104657 | C22 | semidirect |
| 30. #19104657 | C22 | semidirect |
| 33. #19104655 | C22 | semidirect |
| 34. #19104645 | C22 | semidirect |
| 35. C8×Dic163 | C22 | semidirect |
| 135. C163 | #3136 | semidirect |
| 146. C2×#102 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782296 | 2 |
| #23782232 | 2 |
| #23782028 | 2 |
| #23782023 | 2 |
| #23782018 | 2 |
| #23782010 | 2 |
| #23781670 | 2 |
| #23781664 | 2 |
| #23781662 | 2 |
| #23781620 | 2 |
| C2×#102×C163 | 2 |
| #3136 | 163 |