Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. #23782319 | C2 | semidirect |
| 2. #23782011 | C2 | semidirect |
| 3. #23781976 | C2 | semidirect |
| 4. #23781945 | C2 | semidirect |
| 5. #23781899 | C2 | semidirect |
| 6. #23781857 | C2 | semidirect |
| 7. #23781799 | C2 | semidirect |
| 8. C4×#14579684 | C2 | semidirect |
| 9. D4×C163⋊C8 | C2 | semidirect |
| 10. C2×#19104656 | C2 | semidirect |
| 11. D42×C163 | C2 | semidirect |
| 14. C2×#14579684 | C22 | semidirect |
| 15. C22×C163⋊C8 | C22 | semidirect |
| 16. #19104735 | C22 | semidirect |
| 19. #19104709 | C22 | semidirect |
| 20. C4×D652 | C22 | semidirect |
| 21. C2×C4⋊Dic163 | C22 | semidirect |
| 22. #19104668 | C22 | semidirect |
| 23. #19104668 | C22 | semidirect |
| 24. C4⋊(C163⋊C8) | C22 | semidirect |
| 27. #19104656 | C22 | semidirect |
| 28. #19104656 | C22 | semidirect |
| 29. #19104656 | C22 | semidirect |
| 30. #19104655 | C22 | semidirect |
| 31. C22⋊(C163⋊C8) | C22 | semidirect |
| 32. C4×C163⋊C8 | C22 | semidirect |
| 103. D4×C163 | D8 | semidirect |
| 104. D4×C163 | #41 | semidirect |
| 142. C163 | #3294 | semidirect |
| 145. D42 | D163 | semidirect |
| 239. D4 | #14579684 | semidirect |
| 240. D4 | #14579698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782319 | 2 |
| #23782011 | 2 |
| #23781976 | 2 |
| #23781945 | 2 |
| #23781899 | 2 |
| #23781857 | 2 |
| #23781799 | 2 |
| C4×#14579684 | 2 |
| D4×C163⋊C8 | 2 |
| C2×#19104656 | 2 |
| D42×C163 | 2 |
| #3294 | 163 |