Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
462 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 462 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. #23782372 | C2 | semidirect |
| 2. #23782011 | C2 | semidirect |
| 3. #23781981 | C2 | semidirect |
| 4. #23781955 | C2 | semidirect |
| 5. #23781892 | C2 | semidirect |
| 6. #23781862 | C2 | semidirect |
| 7. #23781816 | C2 | semidirect |
| 8. C4×#14579687 | C2 | semidirect |
| 9. D4×C163⋊C8 | C2 | semidirect |
| 10. C2×#19104656 | C2 | semidirect |
| 13. C2×#14579687 | C22 | semidirect |
| 14. C22×C163⋊C8 | C22 | semidirect |
| 15. #19104735 | C22 | semidirect |
| 17. #19104714 | C22 | semidirect |
| 19. C4×Dic326 | C22 | semidirect |
| 21. C2×C4⋊Dic163 | C22 | semidirect |
| 22. #19104666 | C22 | semidirect |
| 23. #19104666 | C22 | semidirect |
| 24. C4⋊(C163⋊C8) | C22 | semidirect |
| 25. #19104658 | C22 | semidirect |
| 28. #19104656 | C22 | semidirect |
| 29. #19104656 | C22 | semidirect |
| 30. #19104656 | C22 | semidirect |
| 31. C22⋊(C163⋊C8) | C22 | semidirect |
| 32. C4×C163⋊C8 | C22 | semidirect |
| 100. D4×C163 | SD16 | semidirect |
| 136. C163 | #3295 | semidirect |
| 230. D4 | #14579687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782372 | 2 |
| #23782011 | 2 |
| #23781981 | 2 |
| #23781955 | 2 |
| #23781892 | 2 |
| #23781862 | 2 |
| #23781816 | 2 |
| C4×#14579687 | 2 |
| D4×C163⋊C8 | 2 |
| C2×#19104656 | 2 |
| D42×C163 | 2 |
| #3295 | 163 |