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×#19104768 | C2 | semidirect |
| 3. C22×#14579688 | C2 | semidirect |
| 4. #23782236 | C2 | semidirect |
| 5. #23781829 | C2 | semidirect |
| 6. #23781818 | C2 | semidirect |
| 7. #23781671 | C2 | semidirect |
| 8. #23781662 | C2 | semidirect |
| 9. #408×C163 | C2 | semidirect |
| 15. C22×Dic326 | C22 | semidirect |
| 21. C2×Dic652 | C22 | semidirect |
| 23. C2×#14579688 | C22 | semidirect |
| 24. C2×#14579688 | C22 | semidirect |
| 28. #19104714 | C22 | semidirect |
| 29. #19104694 | C22 | semidirect |
| 30. #19104660 | C22 | semidirect |
| 31. #19104657 | C22 | semidirect |
| 32. #19104657 | C22 | semidirect |
| 34. C2×M16×C163 | C22 | semidirect |
| 35. C22×C8×C163 | C22 | semidirect |
| 36. C22⋊C8×C163 | C22 | semidirect |
| 146. C163 | #3009 | semidirect |
| 156. #408 | D163 | semidirect |
| 173. C2×M16 | C2×D163 | semidirect |
| 174. C22×C8 | C2×D163 | semidirect |
| 183. 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×#19104781 | 2 |
| C2×#19104768 | 2 |
| C22×#14579688 | 2 |
| #23782236 | 2 |
| #23781829 | 2 |
| #23781818 | 2 |
| #23781671 | 2 |
| #23781662 | 2 |
| #408×C163 | 2 |
| #3009 | 163 |