Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
794 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 135 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. #123×D163 | C2 | semidirect |
| 3. #23781856 | C2 | semidirect |
| 4. #23781855 | C2 | semidirect |
| 5. #23781854 | C2 | semidirect |
| 6. #99×D163 | C2 | semidirect |
| 7. #458×C163 | C2 | semidirect |
| 14. C22×C4×D163 | C22 | semidirect |
| 16. #19104719 | C22 | semidirect |
| 17. #19104718 | C22 | semidirect |
| 19. #19104716 | C22 | semidirect |
| 22. C22⋊C4×D163 | C22 | semidirect |
| 23. #19104650 | C22 | semidirect |
| 24. #19104649 | C22 | semidirect |
| 26. #123×C163 | C22 | semidirect |
| 27. #99×C163 | C22 | semidirect |
| 48. C22×Dic163 | C23 | semidirect |
| 58. C22⋊Dic163 | C23 | semidirect |
| 65. C22×C4×C163 | C23 | semidirect |
| 68. C22⋊C4×C163 | C23 | semidirect |
| 129. D163 | #458 | direct (N × H) |
| 130. C163 | C2×#458 | semidirect |
| 137. #458 | D163 | direct (N × H) |
| 152. #123 | C2×D163 | semidirect |
| 158. #99 | C2×D163 | semidirect |
| 188. C22×C4 | C22×D163 | semidirect |
| 199. C22⋊C4 | C22×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(5,𝔽2)×D163 | 2 |
| #123×D163 | 2 |
| #23781856 | 2 |
| #23781855 | 2 |
| #23781854 | 2 |
| #99×D163 | 2 |
| #458×C163 | 2 |
| C2×#458 | 163 |