Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23782003 | C2 | semidirect |
| 3. #23781962 | C2 | semidirect |
| 4. #23781867 | C2 | semidirect |
| 6. #23781763 | C2 | semidirect |
| 7. C4×#14579686 | C2 | semidirect |
| 8. #23781726 | C2 | semidirect |
| 9. #541×C163 | C2 | semidirect |
| 18. #19104668 | C22 | semidirect |
| 19. #19104666 | C22 | semidirect |
| 20. C4⋊(C163⋊C8) | C22 | semidirect |
| 21. #19104659 | C22 | semidirect |
| 22. #19104659 | C22 | semidirect |
| 26. #19104646 | C22 | semidirect |
| 27. C4×C163⋊C8 | C22 | semidirect |
| 28. C4⋊Q8×C163 | C22 | semidirect |
| 31. #125×C163 | C22 | semidirect |
| 33. C4×Q8×C163 | C22 | semidirect |
| 102. C163 | #3123 | semidirect |
| 104. #541 | D163 | semidirect |
| 116. C4⋊Q8 | C2×D163 | semidirect |
| 119. #125 | C2×D163 | semidirect |
| 121. C4×Q8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782139 | 2 |
| #23782003 | 2 |
| #23781962 | 2 |
| #23781867 | 2 |
| #23781815 | 2 |
| #23781763 | 2 |
| C4×#14579686 | 2 |
| #23781726 | 2 |
| #541×C163 | 2 |
| #3123 | 163 |