Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#19104761 | C2 | semidirect |
| 2. C2×#19104755 | C2 | semidirect |
| 3. #23782145 | C2 | semidirect |
| 4. #23781884 | C2 | semidirect |
| 5. #23781877 | C2 | semidirect |
| 6. #23781862 | C2 | semidirect |
| 7. #23781857 | C2 | semidirect |
| 8. #23781692 | C2 | semidirect |
| 9. #23781666 | C2 | semidirect |
| 10. C2×#19104656 | C2 | semidirect |
| 11. #535×C163 | C2 | semidirect |
| 15. C2×#14579689 | C22 | semidirect |
| 17. C2×#14579687 | C22 | semidirect |
| 18. C2×#14579686 | C22 | semidirect |
| 20. C2×#14579684 | C22 | semidirect |
| 23. C4×Dic326 | C22 | semidirect |
| 24. C4×D652 | C22 | semidirect |
| 29. C4⋊(C163⋊C8) | C22 | semidirect |
| 30. C4⋊(C163⋊C8) | C22 | semidirect |
| 31. #19104659 | C22 | semidirect |
| 34. #19104656 | C22 | semidirect |
| 44. #14579699 | D4 | semidirect |
| 154. C163 | #3045 | semidirect |
| 158. #535 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104761 | 2 |
| C2×#19104755 | 2 |
| #23782145 | 2 |
| #23781884 | 2 |
| #23781877 | 2 |
| #23781862 | 2 |
| #23781857 | 2 |
| #23781692 | 2 |
| #23781666 | 2 |
| C2×#19104656 | 2 |
| #535×C163 | 2 |
| #3045 | 163 |