Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19104755 | C2 | semidirect |
| 3. #23782229 | C2 | semidirect |
| 4. #23782146 | C2 | semidirect |
| 5. #23781890 | C2 | semidirect |
| 6. #23781883 | C2 | semidirect |
| 7. #23781864 | C2 | semidirect |
| 8. #23781859 | C2 | semidirect |
| 9. #23781693 | C2 | semidirect |
| 10. C2×#19104655 | C2 | semidirect |
| 11. #417×C163 | C2 | semidirect |
| 16. C2×#14579689 | C22 | semidirect |
| 18. C2×#14579687 | C22 | semidirect |
| 19. C2×#14579686 | C22 | semidirect |
| 21. C2×#14579684 | C22 | semidirect |
| 28. #19104700 | C22 | semidirect |
| 29. #19104697 | C22 | semidirect |
| 34. Dic163⋊C8 | C22 | semidirect |
| 35. Dic163⋊C8 | C22 | semidirect |
| 41. #103×C163 | C22 | semidirect |
| 42. #102×C163 | C22 | semidirect |
| 45. #14579699 | D4 | semidirect |
| 154. C163 | #3045 | semidirect |
| 165. #417 | D163 | semidirect |
| 194. #103 | C2×D163 | semidirect |
| 197. #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×#19104755 | 2 |
| #23782229 | 2 |
| #23782146 | 2 |
| #23781890 | 2 |
| #23781883 | 2 |
| #23781864 | 2 |
| #23781859 | 2 |
| #23781693 | 2 |
| C2×#19104655 | 2 |
| #417×C163 | 2 |
| #3045 | 163 |