Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
794 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 794 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×#19104718 | C2 | semidirect |
| 3. #23781854 | C2 | direct (N × H) |
| 4. C2×#19104650 | C2 | semidirect |
| 5. C2×#19104649 | C2 | semidirect |
| 6. C2×#123×C163 | C2 | semidirect |
| 16. #19104718 | C22 | semidirect |
| 18. C2×C22⋊Dic163 | C22 | semidirect |
| 20. #19104650 | C22 | semidirect |
| 21. #19104649 | C22 | semidirect |
| 23. C23×C4×C163 | C22 | semidirect |
| 25. #123×C163 | C22 | semidirect |
| 28. C2×C22⋊C4×C163 | C22 | semidirect |
| 54. C22⋊Dic163 | C23 | semidirect |
| 68. C22×C4×C163 | C23 | semidirect |
| 72. C22⋊C4×C163 | C23 | semidirect |
| 144. C2×C163 | #458 | semidirect |
| 147. C163 | C2×#458 | semidirect |
| 151. C2×#123 | D163 | semidirect |
| 164. C23×C4 | C2×D163 | semidirect |
| 168. #123 | C2×D163 | semidirect |
| 174. C2×C22⋊C4 | C2×D163 | semidirect |
| 212. C22×C4 | C22×D163 | semidirect |
| 220. C22⋊C4 | C22×D163 | semidirect |
| 293. C2 | #23781854 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104780 | 2 |
| C2×#19104718 | 2 |
| #23781854 | 2 |
| C2×#19104650 | 2 |
| C2×#19104649 | 2 |
| C2×#123×C163 | 2 |
| C2×#458 | 163 |