Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 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 |
|---|---|---|
| 1. C2×#19104763 | C2 | semidirect |
| 2. #23782243 | C2 | semidirect |
| 3. #23782229 | C2 | semidirect |
| 4. #23781918 | C2 | semidirect |
| 5. #23781911 | C2 | semidirect |
| 6. #23781901 | C2 | semidirect |
| 7. #23781894 | C2 | semidirect |
| 8. #23781707 | C2 | semidirect |
| 9. #23781662 | C2 | semidirect |
| 10. C2×#19104657 | C2 | semidirect |
| 11. C2×#131×C163 | C2 | semidirect |
| 19. #19104714 | C22 | semidirect |
| 23. #19104709 | C22 | semidirect |
| 29. #19104669 | C22 | semidirect |
| 30. #19104667 | C22 | semidirect |
| 31. #19104660 | C22 | semidirect |
| 32. #19104660 | C22 | semidirect |
| 35. #19104657 | C22 | semidirect |
| 36. #19104657 | C22 | semidirect |
| 40. C2×M16×C163 | C22 | semidirect |
| 42. C22×C8×C163 | C22 | semidirect |
| 79. M16×C163 | D4 | semidirect |
| 151. C163 | #3062 | semidirect |
| 154. C2×#131 | D163 | semidirect |
| 172. C2×M16 | C2×D163 | semidirect |
| 174. C22×C8 | C2×D163 | semidirect |
| 220. M16 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104763 | 2 |
| #23782243 | 2 |
| #23782229 | 2 |
| #23781918 | 2 |
| #23781911 | 2 |
| #23781901 | 2 |
| #23781894 | 2 |
| #23781707 | 2 |
| #23781662 | 2 |
| C2×#19104657 | 2 |
| C2×#131×C163 | 2 |
| #3062 | 163 |