Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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×#19104755 | C2 | semidirect |
| 2. #23782232 | C2 | semidirect |
| 3. #23782148 | C2 | semidirect |
| 4. #23781885 | C2 | semidirect |
| 5. #23781878 | C2 | semidirect |
| 6. #23781863 | C2 | semidirect |
| 7. #23781858 | C2 | semidirect |
| 8. #23781693 | C2 | semidirect |
| 9. #23781667 | C2 | semidirect |
| 10. C2×#19104656 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C163 | C2 | semidirect |
| 14. C2×#14579689 | C22 | semidirect |
| 15. C2×#14579687 | C22 | semidirect |
| 16. C2×#14579686 | C22 | semidirect |
| 17. C2×#14579684 | C22 | semidirect |
| 24. Q8×Dic163 | C22 | semidirect |
| 26. D4×Dic163 | C22 | semidirect |
| 31. Dic163⋊C8 | C22 | semidirect |
| 32. Dic163⋊C8 | C22 | semidirect |
| 33. #19104660 | C22 | semidirect |
| 34. #19104657 | C22 | semidirect |
| 73. #41×C163 | D4 | semidirect |
| 154. C163 | #3045 | semidirect |
| 156. C2×AGL(1,ℤ/8) | D163 | semidirect |
| 202. #41 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104755 | 2 |
| #23782232 | 2 |
| #23782148 | 2 |
| #23781885 | 2 |
| #23781878 | 2 |
| #23781863 | 2 |
| #23781858 | 2 |
| #23781693 | 2 |
| #23781667 | 2 |
| C2×#19104656 | 2 |
| C2×AGL(1,ℤ/8)×C163 | 2 |
| #3045 | 163 |