Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
378 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. C2×#19104691 | C2 | semidirect |
| 5. #23781526 | C2 | semidirect |
| 6. #23781432 | C2 | semidirect |
| 7. #342×C163 | C2 | semidirect |
| 15. C2×C4⋊Dic163 | C4 | semidirect |
| 19. C2×(C2×D163)⋊C4 | C4 | semidirect |
| 139. C163 | #1899 | semidirect |
| 147. #342 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104719 | 2 |
| C2×#19104691 | 2 |
| C2×#19104649 | 2 |
| #23781526 | 2 |
| #23781432 | 2 |
| #342×C163 | 2 |
| #1899 | 163 |