Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 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×#19104755 | C2 | semidirect |
| 2. C2×#19104743 | C2 | semidirect |
| 3. #23782246 | C2 | semidirect |
| 4. #23782243 | C2 | semidirect |
| 5. #23781914 | C2 | semidirect |
| 6. #23781910 | C2 | semidirect |
| 7. #23781905 | C2 | semidirect |
| 8. #23781900 | C2 | semidirect |
| 9. C2×#19104668 | C2 | semidirect |
| 10. #23781667 | C2 | semidirect |
| 11. #417×C163 | C2 | semidirect |
| 63. C2×C163⋊C8 | D4 | semidirect |
| 152. C163 | #3061 | semidirect |
| 164. #417 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104755 | 2 |
| C2×#19104743 | 2 |
| #23782246 | 2 |
| #23782243 | 2 |
| #23781914 | 2 |
| #23781910 | 2 |
| #23781905 | 2 |
| #23781900 | 2 |
| C2×#19104668 | 2 |
| #23781667 | 2 |
| #417×C163 | 2 |
| #3061 | 163 |