Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4×D652 | C2 | semidirect |
| 2. #23781993 | C2 | semidirect |
| 3. #23781976 | C2 | semidirect |
| 4. #23781962 | C2 | semidirect |
| 5. #23781877 | C2 | semidirect |
| 6. #23781815 | C2 | semidirect |
| 8. #23781775 | C2 | semidirect |
| 9. #23781763 | C2 | semidirect |
| 10. #23781722 | C2 | semidirect |
| 11. #529×C163 | C2 | semidirect |
| 22. #19104668 | C22 | semidirect |
| 23. #19104666 | C22 | semidirect |
| 24. C4⋊(C163⋊C8) | C22 | semidirect |
| 25. #19104659 | C22 | semidirect |
| 26. #19104656 | C22 | semidirect |
| 31. #19104646 | C22 | semidirect |
| 33. #125×C163 | C22 | semidirect |
| 34. #124×C163 | C22 | semidirect |
| 38. C4×Q8×C163 | C22 | semidirect |
| 40. C4×D4×C163 | C22 | semidirect |
| 140. C163 | #3114 | semidirect |
| 142. #529 | D163 | semidirect |
| 158. #125 | C2×D163 | semidirect |
| 159. #124 | C2×D163 | semidirect |
| 163. C4×Q8 | C2×D163 | semidirect |
| 169. C4×D4 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D652 | 2 |
| #23781993 | 2 |
| #23781976 | 2 |
| #23781962 | 2 |
| #23781877 | 2 |
| #23781815 | 2 |
| #23781798 | 2 |
| #23781775 | 2 |
| #23781763 | 2 |
| #23781722 | 2 |
| #529×C163 | 2 |
| #3114 | 163 |