Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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. #23782241 | C2 | semidirect |
| 4. #23782145 | C2 | semidirect |
| 5. #23781888 | C2 | semidirect |
| 6. #23781881 | C2 | semidirect |
| 7. #23781876 | C2 | semidirect |
| 8. #23781871 | C2 | semidirect |
| 9. #23781667 | C2 | semidirect |
| 10. C2×#19104660 | C2 | semidirect |
| 11. #424×C163 | C2 | semidirect |
| 146. C163 | #3046 | semidirect |
| 156. #424 | 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×#19104757 | 2 |
| #23782241 | 2 |
| #23782145 | 2 |
| #23781888 | 2 |
| #23781881 | 2 |
| #23781876 | 2 |
| #23781871 | 2 |
| #23781667 | 2 |
| C2×#19104660 | 2 |
| #424×C163 | 2 |
| #3046 | 163 |