Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
472 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 472 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. C2×#19104741 | C2 | semidirect |
| 3. #23781783 | C2 | direct (N × H) |
| 4. C2×#19104671 | C2 | semidirect |
| 5. C2×#19104663 | C2 | semidirect |
| 6. C2×C4×C8×C163 | C2 | semidirect |
| 8. #19104757 | C4 | semidirect |
| 10. C2×Dic652 | C4 | semidirect |
| 11. C2×#14579688 | C4 | semidirect |
| 12. C2×D1304 | C4 | semidirect |
| 14. #19104741 | C22 | semidirect |
| 18. #19104671 | C22 | semidirect |
| 19. #19104663 | C22 | semidirect |
| 23. C4×C8×C163 | C22 | semidirect |
| 32. Dic652 | C2×C4 | semidirect |
| 33. #14579688 | C2×C4 | semidirect |
| 34. D1304 | C2×C4 | semidirect |
| 90. C2×C163 | #443 | semidirect |
| 93. C163 | C2×#443 | semidirect |
| 100. C2×C4×C8 | D163 | semidirect |
| 117. C4×C8 | C2×D163 | semidirect |
| 185. C2 | #23781783 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104757 | 2 |
| C2×#19104741 | 2 |
| #23781783 | 2 |
| C2×#19104671 | 2 |
| C2×#19104663 | 2 |
| C2×C4×C8×C163 | 2 |
| C2×#443 | 163 |