Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 752 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×#19104766 | C2 | semidirect |
| 3. #23782239 | C2 | semidirect |
| 4. #23781824 | C2 | semidirect |
| 5. #23781814 | C2 | semidirect |
| 6. #23781670 | C2 | semidirect |
| 7. #23781662 | C2 | semidirect |
| 8. #23781631 | C2 | semidirect |
| 9. C22×SD16×C163 | C2 | semidirect |
| 20. C2×#14579689 | C22 | semidirect |
| 21. C2×#14579686 | C22 | semidirect |
| 22. C2×#14579683 | C22 | semidirect |
| 26. #19104711 | C22 | semidirect |
| 27. #19104694 | C22 | semidirect |
| 28. #19104660 | C22 | semidirect |
| 29. #19104657 | C22 | semidirect |
| 30. #19104656 | C22 | semidirect |
| 31. (C2×D163)⋊C8 | C22 | semidirect |
| 32. C22×Q8×C163 | C22 | semidirect |
| 35. C2×SD16×C163 | C22 | semidirect |
| 36. C22×C8×C163 | C22 | semidirect |
| 146. C163 | #3009 | semidirect |
| 150. C22×SD16 | D163 | semidirect |
| 163. C22×Q8 | C2×D163 | semidirect |
| 172. C2×SD16 | C2×D163 | semidirect |
| 174. C22×C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104780 | 2 |
| C2×#19104766 | 2 |
| #23782239 | 2 |
| #23781824 | 2 |
| #23781814 | 2 |
| #23781670 | 2 |
| #23781662 | 2 |
| #23781631 | 2 |
| C22×SD16×C163 | 2 |
| #3009 | 163 |