Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
612 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 101 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×#19104650 | C2 | semidirect |
| 3. C2×#19104649 | C2 | semidirect |
| 4. #23781526 | C2 | semidirect |
| 5. C2×#99×C163 | C2 | semidirect |
| 10. C22×Dic326 | C4 | semidirect |
| 11. C22×C22⋊D163 | C4 | semidirect |
| 13. C23×Dic163 | C4 | semidirect |
| 15. C22×C4×D163 | C4 | semidirect |
| 134. C163 | #1782 | semidirect |
| 139. C2×#99 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579698 | 2 |
| C2×#19104650 | 2 |
| C2×#19104649 | 2 |
| #23781526 | 2 |
| C2×#99×C163 | 2 |
| #1782 | 163 |