Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19104768 | C2 | semidirect |
| 3. C22×#14579689 | C2 | semidirect |
| 4. #23782241 | C2 | semidirect |
| 5. #23781830 | C2 | semidirect |
| 6. #23781822 | C2 | semidirect |
| 7. #23781659 | C2 | semidirect |
| 8. #23781633 | C2 | semidirect |
| 9. #419×C163 | C2 | semidirect |
| 140. C163 | #3011 | semidirect |
| 148. #419 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104783 | 2 |
| C2×#19104768 | 2 |
| C22×#14579689 | 2 |
| #23782241 | 2 |
| #23781830 | 2 |
| #23781822 | 2 |
| #23781659 | 2 |
| #23781633 | 2 |
| #419×C163 | 2 |
| #3011 | 163 |