Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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×#19104765 | C2 | semidirect |
| 2. C2×#19104722 | C2 | semidirect |
| 3. #41×Dic163 | C2 | semidirect |
| 4. #23781885 | C2 | semidirect |
| 5. #23781878 | C2 | semidirect |
| 6. #23781688 | C2 | semidirect |
| 7. #23781675 | C2 | semidirect |
| 8. #23781670 | C2 | semidirect |
| 12. C2×#14579689 | C22 | semidirect |
| 13. C2×#14579687 | C22 | semidirect |
| 18. Q8×Dic163 | C22 | semidirect |
| 20. D4×Dic163 | C22 | semidirect |
| 26. Dic163⋊C8 | C22 | semidirect |
| 27. #19104660 | C22 | semidirect |
| 125. C163 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104765 | 2 |
| C2×#19104722 | 2 |
| #41×Dic163 | 2 |
| #23781885 | 2 |
| #23781878 | 2 |
| #23781688 | 2 |
| #23781675 | 2 |
| #23781670 | 2 |
| C2×AGL(1,ℤ/8)×C163 | 2 |
| #3040 | 163 |