Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
280 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 65 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×#19104652 | C2 | semidirect |
| 3. #23781454 | C2 | semidirect |
| 4. #23781451 | C2 | semidirect |
| 5. C2×#99×C163 | C2 | semidirect |
| 6. C22×C22⋊D163 | C4 | semidirect |
| 9. #19104716 | C4 | semidirect |
| 14. #19104703 | C4 | semidirect |
| 16. C2×C22⋊Dic163 | C4 | semidirect |
| 23. C23×D163 | C2×C4 | semidirect |
| 31. C22×Dic163 | C2×C4 | semidirect |
| 40. C22⋊Dic163 | C2×C4 | semidirect |
| 41. C22⋊Dic163 | C2×C4 | semidirect |
| 126. C163 | #2121 | semidirect |
| 130. C2×#99 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782224 | 2 |
| C2×#19104652 | 2 |
| #23781454 | 2 |
| #23781451 | 2 |
| C2×#99×C163 | 2 |
| #2121 | 163 |