Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 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×#19104754 | C2 | semidirect |
| 2. #23782309 | C2 | semidirect |
| 3. #23782048 | C2 | semidirect |
| 4. #23781906 | C2 | semidirect |
| 5. #23781898 | C2 | semidirect |
| 6. #23781878 | C2 | semidirect |
| 7. #23781816 | C2 | semidirect |
| 8. #23781807 | C2 | semidirect |
| 9. D8×Dic163 | C2 | semidirect |
| 10. C8×C22⋊D163 | C2 | semidirect |
| 11. C22×D8×C163 | C2 | semidirect |
| 12. C2×#14579698 | C22 | semidirect |
| 14. C2×Dic652 | C22 | semidirect |
| 15. C2×#14579687 | C22 | semidirect |
| 16. C2×#14579687 | C22 | semidirect |
| 17. C2×C8×D163 | C22 | semidirect |
| 18. #19104722 | C22 | semidirect |
| 22. #19104706 | C22 | semidirect |
| 24. D4×Dic163 | C22 | semidirect |
| 27. #19104669 | C22 | semidirect |
| 28. Dic163⋊C8 | C22 | semidirect |
| 29. #19104660 | C22 | semidirect |
| 30. #19104656 | C22 | semidirect |
| 31. #19104656 | C22 | semidirect |
| 33. (C2×D163)⋊C8 | C22 | semidirect |
| 34. C8×Dic163 | C22 | semidirect |
| 76. D8×C163 | D4 | semidirect |
| 123. C22×C163 | #135 | semidirect |
| 143. C163 | #3280 | semidirect |
| 146. C22×D8 | D163 | semidirect |
| 206. D8 | C22⋊D163 | semidirect |
| 270. C22 | #19104754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104754 | 2 |
| #23782309 | 2 |
| #23782048 | 2 |
| #23781906 | 2 |
| #23781898 | 2 |
| #23781878 | 2 |
| #23781816 | 2 |
| #23781807 | 2 |
| D8×Dic163 | 2 |
| C8×C22⋊D163 | 2 |
| C22×D8×C163 | 2 |
| #3280 | 163 |