Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
484 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×#19104758 | C2 | semidirect |
| 2. C2×#19104757 | C2 | semidirect |
| 3. #23782317 | C2 | semidirect |
| 4. #23782043 | C2 | semidirect |
| 5. #23781907 | C2 | semidirect |
| 6. #23781869 | C2 | semidirect |
| 7. #23781830 | C2 | semidirect |
| 8. #23781825 | C2 | semidirect |
| 9. #23781747 | C2 | semidirect |
| 10. C8×C22⋊D163 | C2 | semidirect |
| 11. #467×C163 | C2 | semidirect |
| 58. D1304 | D4 | semidirect |
| 129. Dic163 | #135 | semidirect |
| 136. C163 | #3283 | semidirect |
| 143. #467 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104758 | 2 |
| C2×#19104757 | 2 |
| #23782317 | 2 |
| #23782043 | 2 |
| #23781907 | 2 |
| #23781869 | 2 |
| #23781830 | 2 |
| #23781825 | 2 |
| #23781747 | 2 |
| C8×C22⋊D163 | 2 |
| #467×C163 | 2 |
| #3283 | 163 |