Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 3. #23781763 | C2 | semidirect |
| 4. C4×#14579686 | C2 | semidirect |
| 5. #23781701 | C2 | semidirect |
| 6. #23781674 | C2 | semidirect |
| 8. #23781621 | C2 | semidirect |
| 9. #519×C163 | C2 | semidirect |
| 11. C2×#14579686 | C4 | semidirect |
| 20. #19104668 | C22 | semidirect |
| 21. #19104666 | C22 | semidirect |
| 22. #19104659 | C22 | semidirect |
| 24. #19104646 | C22 | semidirect |
| 25. C4×C163⋊C8 | C22 | semidirect |
| 28. C4×Q8×C163 | C22 | semidirect |
| 38. #14579686 | C2×C4 | semidirect |
| 39. #14579686 | C2×C4 | semidirect |
| 41. C2×C163⋊C8 | C2×C4 | semidirect |
| 51. C2×Q8×C163 | C2×C4 | semidirect |
| 103. C163 | #2949 | semidirect |
| 106. #519 | D163 | semidirect |
| 122. C4×Q8 | C2×D163 | semidirect |
| 139. C2×Q8 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579686 | 2 |
| #23782139 | 2 |
| #23781763 | 2 |
| C4×#14579686 | 2 |
| #23781701 | 2 |
| #23781674 | 2 |
| #23781669 | 2 |
| #23781621 | 2 |
| #519×C163 | 2 |
| #2949 | 163 |