Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
418 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23782400 | C2 | semidirect |
| 2. #23782052 | C2 | semidirect |
| 3. #23782041 | C2 | semidirect |
| 4. #23781880 | C2 | semidirect |
| 5. #23781862 | C2 | semidirect |
| 6. #23781860 | C2 | semidirect |
| 7. #23781857 | C2 | semidirect |
| 8. #23781796 | C2 | semidirect |
| 9. #23781775 | C2 | semidirect |
| 10. C4×#14579687 | C2 | semidirect |
| 11. #550×C163 | C2 | semidirect |
| 89. C163⋊C8 | #41 | semidirect |
| 134. C163 | #3399 | semidirect |
| 137. #550 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782400 | 2 |
| #23782052 | 2 |
| #23782041 | 2 |
| #23781880 | 2 |
| #23781862 | 2 |
| #23781860 | 2 |
| #23781857 | 2 |
| #23781796 | 2 |
| #23781775 | 2 |
| C4×#14579687 | 2 |
| #550×C163 | 2 |
| #3399 | 163 |