Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
374 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 374 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. #23782388 | C2 | semidirect |
| 3. #23782068 | C2 | semidirect |
| 4. #23781999 | C2 | semidirect |
| 5. #23781991 | C2 | semidirect |
| 6. #23781946 | C2 | semidirect |
| 7. #23781914 | C2 | semidirect |
| 8. C4×#14579686 | C2 | semidirect |
| 9. #23781742 | C2 | semidirect |
| 10. #23781704 | C2 | semidirect |
| 11. #475×C163 | C2 | semidirect |
| 89. C163⋊C8 | #41 | semidirect |
| 122. C163 | #3353 | semidirect |
| 129. #475 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782388 | 2 |
| #23782318 | 2 |
| #23782068 | 2 |
| #23781999 | 2 |
| #23781991 | 2 |
| #23781946 | 2 |
| #23781914 | 2 |
| C4×#14579686 | 2 |
| #23781742 | 2 |
| #23781704 | 2 |
| #475×C163 | 2 |
| #3353 | 163 |