Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
800 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 249 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. #23782140 | C2 | semidirect |
| 3. #23781638 | C2 | semidirect |
| 4. C2×#19104649 | C2 | semidirect |
| 5. #518×C163 | C2 | semidirect |
| 9. C2×#14579698 | C4 | semidirect |
| 11. C2×D4×D163 | C4 | semidirect |
| 13. #19104694 | C22 | semidirect |
| 14. C2×C22⋊Dic163 | C22 | semidirect |
| 15. #19104649 | C22 | semidirect |
| 18. #117×C163 | C22 | semidirect |
| 19. C2×C22⋊C4×C163 | C22 | semidirect |
| 20. C23×D163 | C2×C4 | semidirect |
| 24. C2×Dic326 | C2×C4 | semidirect |
| 25. C2×D652 | C2×C4 | semidirect |
| 28. C2×C22⋊D163 | C2×C4 | semidirect |
| 32. C22×Dic163 | C2×C4 | semidirect |
| 33. C2×C4×D163 | C2×C4 | semidirect |
| 93. C163 | #2883 | semidirect |
| 97. #518 | D163 | semidirect |
| 110. #117 | C2×D163 | semidirect |
| 112. C2×C22⋊C4 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104780 | 2 |
| #23782140 | 2 |
| #23781638 | 2 |
| C2×#19104649 | 2 |
| #518×C163 | 2 |
| #2883 | 163 |