Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. #23781947 | C2 | semidirect |
| 5. #23781876 | C2 | semidirect |
| 6. #23781875 | C2 | semidirect |
| 8. #23781771 | C2 | semidirect |
| 9. #23781769 | C2 | semidirect |
| 11. #475×C163 | C2 | semidirect |
| 132. C163 | #3113 | semidirect |
| 138. #475 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782220 | 2 |
| C4×Q8×D163 | 2 |
| #23781997 | 2 |
| #23781947 | 2 |
| #23781876 | 2 |
| #23781875 | 2 |
| #23781822 | 2 |
| #23781771 | 2 |
| #23781769 | 2 |
| #23781721 | 2 |
| #475×C163 | 2 |
| #3113 | 163 |