Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19104766 | C2 | semidirect |
| 3. C2×#19104724 | C2 | semidirect |
| 4. #23782133 | C2 | semidirect |
| 5. #23781890 | C2 | semidirect |
| 6. #23781883 | C2 | semidirect |
| 7. #23781688 | C2 | semidirect |
| 8. #23781669 | C2 | semidirect |
| 9. #419×C163 | C2 | semidirect |
| 14. C2×#14579689 | C22 | semidirect |
| 16. C2×#14579686 | C22 | semidirect |
| 22. #19104700 | C22 | semidirect |
| 23. #19104697 | C22 | semidirect |
| 29. Dic163⋊C8 | C22 | semidirect |
| 34. #103×C163 | C22 | semidirect |
| 125. C163 | #3040 | semidirect |
| 134. #419 | D163 | semidirect |
| 159. #103 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104766 | 2 |
| C2×#19104763 | 2 |
| C2×#19104724 | 2 |
| #23782133 | 2 |
| #23781890 | 2 |
| #23781883 | 2 |
| #23781688 | 2 |
| #23781669 | 2 |
| #419×C163 | 2 |
| #3040 | 163 |