Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23782216 | C2 | semidirect |
| 2. #23782194 | C2 | semidirect |
| 3. #23782071 | C2 | semidirect |
| 4. #23782055 | C2 | semidirect |
| 5. #23782030 | C2 | semidirect |
| 6. #23781917 | C2 | semidirect |
| 7. #23781914 | C2 | semidirect |
| 8. #23781750 | C2 | semidirect |
| 9. #23781745 | C2 | semidirect |
| 10. #23781617 | C2 | semidirect |
| 11. #489×C163 | C2 | semidirect |
| 100. C163⋊C8 | #41 | semidirect |
| 137. C163 | #3171 | semidirect |
| 144. #489 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782216 | 2 |
| #23782194 | 2 |
| #23782071 | 2 |
| #23782055 | 2 |
| #23782030 | 2 |
| #23781917 | 2 |
| #23781914 | 2 |
| #23781750 | 2 |
| #23781745 | 2 |
| #23781617 | 2 |
| #489×C163 | 2 |
| #3171 | 163 |