Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
376 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 3. #23781975 | C2 | semidirect |
| 4. #23781974 | C2 | semidirect |
| 5. #23781961 | C2 | semidirect |
| 6. #23781960 | C2 | semidirect |
| 7. #23781947 | C2 | semidirect |
| 11. #475×C163 | C2 | semidirect |
| 47. Q8×D163 | Q8 | semidirect |
| 130. C163 | #3078 | semidirect |
| 139. #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 |
| #23781975 | 2 |
| #23781974 | 2 |
| #23781961 | 2 |
| #23781960 | 2 |
| #23781947 | 2 |
| #23781704 | 2 |
| #23781687 | 2 |
| #23781672 | 2 |
| #475×C163 | 2 |
| #3078 | 163 |