Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
638 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 638 conjugacy classes of subgroups — too many to draw. Only its 73 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. #23782227 | C2 | semidirect |
| 2. C2×#19104704 | C2 | semidirect |
| 3. C2×#19104649 | C2 | semidirect |
| 4. #23781432 | C2 | semidirect |
| 5. #379×C163 | C2 | semidirect |
| 20. C23×D163 | D4 | semidirect |
| 31. C22×Dic163 | D4 | semidirect |
| 35. C22⋊Dic163 | D4 | semidirect |
| 42. C24×C163 | D4 | semidirect |
| 45. C22×C4×C163 | D4 | semidirect |
| 120. C163 | #2021 | semidirect |
| 125. #379 | D163 | semidirect |
| 147. C24 | D652 | semidirect |
| 161. C22×C4 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782227 | 2 |
| C2×#19104704 | 2 |
| C2×#19104649 | 2 |
| #23781432 | 2 |
| #379×C163 | 2 |
| #2021 | 163 |