Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 2. #23782139 | C2 | semidirect |
| 3. #23781775 | C2 | semidirect |
| 4. C4×#14579684 | C2 | semidirect |
| 5. #23781701 | C2 | semidirect |
| 6. #23781670 | C2 | semidirect |
| 7. #23781669 | C2 | semidirect |
| 8. #23781621 | C2 | semidirect |
| 9. #518×C163 | C2 | semidirect |
| 11. C2×#14579684 | C4 | semidirect |
| 16. C4×D652 | C22 | semidirect |
| 20. #19104668 | C22 | semidirect |
| 21. #19104666 | C22 | semidirect |
| 22. #19104656 | C22 | semidirect |
| 23. #19104655 | C22 | semidirect |
| 24. #19104646 | C22 | semidirect |
| 25. C4×C163⋊C8 | C22 | semidirect |
| 28. C4×D4×C163 | C22 | semidirect |
| 35. C2×D652 | C2×C4 | semidirect |
| 38. #14579684 | C2×C4 | semidirect |
| 39. #14579684 | C2×C4 | semidirect |
| 41. C2×C163⋊C8 | C2×C4 | semidirect |
| 52. C2×D4×C163 | C2×C4 | semidirect |
| 108. C163 | #2948 | semidirect |
| 112. #518 | D163 | semidirect |
| 129. C4×D4 | C2×D163 | semidirect |
| 149. C2×D4 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579684 | 2 |
| #23782139 | 2 |
| #23781775 | 2 |
| C4×#14579684 | 2 |
| #23781701 | 2 |
| #23781670 | 2 |
| #23781669 | 2 |
| #23781621 | 2 |
| #518×C163 | 2 |
| #2948 | 163 |