Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
5956 conjugacy classes of subgroups; only the 3205 normal subgroups are shown.
This group has 5956 conjugacy classes of subgroups — too many to draw. Only its 3205 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. #23782500 | C2 | direct (N × H) |
| 2. C2×#19104782 | C2 | semidirect |
| 3. C2×#19104780 | C2 | semidirect |
| 4. C22×#14579698 | C2 | semidirect |
| 5. C2×#41×D163 | C2 | semidirect |
| 6. C2×H(5,𝔽2)×C163 | C2 | semidirect |
| 7. #19104782 | C22 | semidirect |
| 8. #19104780 | C22 | semidirect |
| 9. C2×#14579700 | C22 | semidirect |
| 10. C2×#14579699 | C22 | semidirect |
| 11. C2×#14579698 | C22 | semidirect |
| 12. C2×#14579698 | C22 | semidirect |
| 13. C2×#14579698 | C22 | semidirect |
| 14. #41×D163 | C22 | semidirect |
| 15. C22×Dic326 | C22 | semidirect |
| 16. C2×Q8×D163 | C22 | semidirect |
| 17. C22×C22⋊D163 | C22 | semidirect |
| 18. C2×D4×D163 | C22 | semidirect |
| 19. C23×Dic163 | C22 | semidirect |
| 20. C22×C4×D163 | C22 | semidirect |
| 21. H(5,𝔽2)×C163 | C22 | semidirect |
| 22. C2×#41×C163 | C22 | semidirect |
| 23. C22×D4×C163 | C22 | semidirect |
| 25. #14579700 | C23 | semidirect |
| 26. #14579699 | C23 | semidirect |
| 27. #14579698 | C23 | semidirect |
| 28. #14579698 | C23 | semidirect |
| 30. C2×Dic326 | C23 | semidirect |
| 31. Q8×D163 | C23 | semidirect |
| 34. C2×C22⋊D163 | C23 | semidirect |
| 35. D4×D163 | C23 | semidirect |
| 38. C22×Dic163 | C23 | semidirect |
| 41. C2×C4×D163 | C23 | semidirect |
| 43. #41×C163 | C23 | semidirect |
| 46. C2×D4×C163 | C23 | semidirect |
| 78. C2×C163 | #585 | semidirect |
| 81. C163 | C2×#585 | semidirect |
| 86. C2×H(5,𝔽2) | D163 | semidirect |
| 91. H(5,𝔽2) | C2×D163 | semidirect |
| 98. C2×#41 | C2×D163 | semidirect |
| 103. C22×D4 | C2×D163 | semidirect |
| 112. #41 | C22×D163 | semidirect |
| 122. C2×D4 | C22×D163 | semidirect |
| 161. C2 | #23782500 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782500 | 2 |
| C2×#19104782 | 2 |
| C2×#19104780 | 2 |
| C22×#14579698 | 2 |
| C2×#41×D163 | 2 |
| C2×H(5,𝔽2)×C163 | 2 |
| C2×#585 | 163 |