Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
560 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 157 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. #23781603 | C2 | semidirect |
| 3. #23781600 | C2 | semidirect |
| 4. #23781596 | C2 | semidirect |
| 5. #23781593 | C2 | semidirect |
| 6. #23781591 | C2 | semidirect |
| 8. C4×Dic163⋊C4 | C2 | semidirect |
| 9. C4×(C2×D163)⋊C4 | C2 | semidirect |
| 10. C4×C22⋊Dic163 | C2 | semidirect |
| 11. C2×#117×C163 | C2 | semidirect |
| 137. C163 | #2395 | semidirect |
| 140. C2×#117 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D163 | 2 |
| #23781603 | 2 |
| #23781600 | 2 |
| #23781596 | 2 |
| #23781593 | 2 |
| #23781591 | 2 |
| #23781580 | 2 |
| C4×Dic163⋊C4 | 2 |
| C4×(C2×D163)⋊C4 | 2 |
| C4×C22⋊Dic163 | 2 |
| C2×#117×C163 | 2 |
| #2395 | 163 |