Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23782146 | C2 | semidirect |
| 3. #23781992 | C2 | semidirect |
| 4. #23781991 | C2 | semidirect |
| 5. #23781985 | C2 | semidirect |
| 6. #23781980 | C2 | semidirect |
| 7. #23781701 | C2 | semidirect |
| 8. #23781671 | C2 | semidirect |
| 9. C2×#19104655 | C2 | semidirect |
| 10. #23781633 | C2 | semidirect |
| 11. #428×C163 | C2 | semidirect |
| 24. #19104693 | C22 | semidirect |
| 25. C4⋊C4×D163 | C22 | semidirect |
| 26. #19104668 | C22 | semidirect |
| 27. #19104668 | C22 | semidirect |
| 28. #19104666 | C22 | semidirect |
| 29. #19104666 | C22 | semidirect |
| 34. (C2×D163)⋊C8 | C22 | semidirect |
| 35. (C2×D163)⋊C8 | C22 | semidirect |
| 39. #107×C163 | C22 | semidirect |
| 40. #106×C163 | C22 | semidirect |
| 134. C163 | #3096 | semidirect |
| 142. #428 | D163 | semidirect |
| 166. #107 | C2×D163 | semidirect |
| 169. #106 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782234 | 2 |
| #23782146 | 2 |
| #23781992 | 2 |
| #23781991 | 2 |
| #23781985 | 2 |
| #23781980 | 2 |
| #23781701 | 2 |
| #23781671 | 2 |
| C2×#19104655 | 2 |
| #23781633 | 2 |
| #428×C163 | 2 |
| #3096 | 163 |