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×#19104763 | C2 | semidirect |
| 2. C22×D1304 | C2 | semidirect |
| 3. #23782234 | C2 | semidirect |
| 4. #23782139 | C2 | semidirect |
| 5. #23781881 | C2 | semidirect |
| 6. #23781861 | C2 | semidirect |
| 7. #23781671 | C2 | semidirect |
| 8. #23781662 | C2 | semidirect |
| 9. #424×C163 | C2 | semidirect |
| 14. C2×#14579688 | C22 | semidirect |
| 17. C2×D1304 | C22 | semidirect |
| 18. #19104732 | C22 | semidirect |
| 19. #19104723 | C22 | semidirect |
| 22. C4×D652 | C22 | semidirect |
| 26. #19104660 | C22 | semidirect |
| 27. #19104657 | C22 | semidirect |
| 28. #19104657 | C22 | semidirect |
| 32. C4⋊C8×C163 | C22 | semidirect |
| 44. C2×D652 | D4 | semidirect |
| 121. C163 | #3041 | semidirect |
| 129. #424 | D163 | semidirect |
| 151. C4⋊C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104763 | 2 |
| C22×D1304 | 2 |
| #23782234 | 2 |
| #23782139 | 2 |
| #23781881 | 2 |
| #23781861 | 2 |
| #23781671 | 2 |
| #23781662 | 2 |
| #424×C163 | 2 |
| #3041 | 163 |