Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19104768 | C2 | semidirect |
| 3. #23782236 | C2 | semidirect |
| 4. #23782146 | C2 | semidirect |
| 5. #23781886 | C2 | semidirect |
| 6. #23781879 | C2 | semidirect |
| 7. #23781874 | C2 | semidirect |
| 8. #23781869 | C2 | semidirect |
| 9. #23781693 | C2 | semidirect |
| 10. C2×#19104658 | C2 | semidirect |
| 11. #417×C163 | C2 | semidirect |
| 146. C163 | #3046 | semidirect |
| 157. #417 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104768 | 2 |
| C2×#19104755 | 2 |
| #23782236 | 2 |
| #23782146 | 2 |
| #23781886 | 2 |
| #23781879 | 2 |
| #23781874 | 2 |
| #23781869 | 2 |
| #23781693 | 2 |
| C2×#19104658 | 2 |
| #417×C163 | 2 |
| #3046 | 163 |