Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
370 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 370 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. #23782390 | C2 | semidirect |
| 3. #23782014 | C2 | semidirect |
| 4. #23781948 | C2 | semidirect |
| 5. #23781947 | C2 | semidirect |
| 8. C8×Dic326 | C2 | semidirect |
| 11. #487×C163 | C2 | semidirect |
| 78. Dic326 | SD16 | semidirect |
| 118. C163 | #3359 | semidirect |
| 123. #487 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782390 | 2 |
| #23782330 | 2 |
| #23782014 | 2 |
| #23781948 | 2 |
| #23781947 | 2 |
| #23781869 | 2 |
| #23781867 | 2 |
| C8×Dic326 | 2 |
| C4×#14579688 | 2 |
| #23781750 | 2 |
| #487×C163 | 2 |
| #3359 | 163 |