Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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×#19104760 | C2 | semidirect |
| 2. C22×#14579684 | C2 | semidirect |
| 3. #23782139 | C2 | semidirect |
| 4. #23781877 | C2 | semidirect |
| 5. #23781857 | C2 | semidirect |
| 6. #23781692 | C2 | semidirect |
| 7. #23781670 | C2 | semidirect |
| 8. #23781661 | C2 | semidirect |
| 9. #535×C163 | C2 | semidirect |
| 12. C2×#14579686 | C22 | semidirect |
| 15. C2×#14579684 | C22 | semidirect |
| 18. C4×D652 | C22 | semidirect |
| 22. C4⋊(C163⋊C8) | C22 | semidirect |
| 23. #19104659 | C22 | semidirect |
| 24. #19104656 | C22 | semidirect |
| 25. #19104656 | C22 | semidirect |
| 28. #127×C163 | C22 | semidirect |
| 29. #124×C163 | C22 | semidirect |
| 36. C2×D652 | D4 | semidirect |
| 121. C163 | #3041 | semidirect |
| 125. #535 | D163 | semidirect |
| 142. #127 | C2×D163 | semidirect |
| 143. #124 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104760 | 2 |
| C22×#14579684 | 2 |
| #23782139 | 2 |
| #23781877 | 2 |
| #23781857 | 2 |
| #23781692 | 2 |
| #23781670 | 2 |
| #23781661 | 2 |
| #535×C163 | 2 |
| #3041 | 163 |