Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
784 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 165 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×#19104760 | C2 | semidirect |
| 2. C22×#14579684 | C2 | semidirect |
| 3. #23782229 | C2 | semidirect |
| 4. #23781810 | C2 | semidirect |
| 5. #23781799 | C2 | semidirect |
| 6. #23781670 | C2 | semidirect |
| 7. #23781661 | C2 | semidirect |
| 8. #23781632 | C2 | semidirect |
| 9. C2×H(5,𝔽2)×C163 | C2 | semidirect |
| 10. C22×D652 | C22 | semidirect |
| 12. C2×#14579686 | C22 | semidirect |
| 14. C2×#14579684 | C22 | semidirect |
| 15. C2×#14579684 | C22 | semidirect |
| 16. C2×#14579683 | C22 | semidirect |
| 17. C22×C163⋊C8 | C22 | semidirect |
| 20. #19104709 | C22 | semidirect |
| 22. #19104694 | C22 | semidirect |
| 23. #19104659 | C22 | semidirect |
| 24. #19104656 | C22 | semidirect |
| 25. #19104656 | C22 | semidirect |
| 26. C22⋊(C163⋊C8) | C22 | semidirect |
| 32. C2×#41×C163 | C22 | semidirect |
| 36. C22×D4×C163 | C22 | semidirect |
| 62. #41×C163 | D4 | semidirect |
| 76. C2×D4×C163 | D4 | semidirect |
| 151. C163 | #3008 | semidirect |
| 153. C2×H(5,𝔽2) | D163 | semidirect |
| 167. C2×#41 | C2×D163 | semidirect |
| 172. C22×D4 | C2×D163 | semidirect |
| 198. #41 | C22⋊D163 | semidirect |
| 217. C2×D4 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104760 | 2 |
| C22×#14579684 | 2 |
| #23782229 | 2 |
| #23781810 | 2 |
| #23781799 | 2 |
| #23781670 | 2 |
| #23781661 | 2 |
| #23781632 | 2 |
| C2×H(5,𝔽2)×C163 | 2 |
| #3008 | 163 |