Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
414 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 414 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. C2×#19104693 | C2 | semidirect |
| 3. #23782009 | C2 | semidirect |
| 4. #23782008 | C2 | semidirect |
| 5. #23781992 | C2 | semidirect |
| 6. #23781991 | C2 | semidirect |
| 7. #23781708 | C2 | semidirect |
| 8. #23781667 | C2 | semidirect |
| 9. #23781664 | C2 | semidirect |
| 10. #23781628 | C2 | semidirect |
| 11. #428×C163 | C2 | semidirect |
| 30. #19104668 | C22 | semidirect |
| 31. #19104666 | C22 | semidirect |
| 32. #19104660 | C22 | semidirect |
| 33. #19104658 | C22 | semidirect |
| 34. #19104657 | C22 | semidirect |
| 35. #19104655 | C22 | semidirect |
| 41. #107×C163 | C22 | semidirect |
| 42. #106×C163 | C22 | semidirect |
| 152. C163 | #3093 | semidirect |
| 161. #428 | D163 | semidirect |
| 187. #107 | C2×D163 | semidirect |
| 189. #106 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782177 | 2 |
| C2×#19104693 | 2 |
| #23782009 | 2 |
| #23782008 | 2 |
| #23781992 | 2 |
| #23781991 | 2 |
| #23781708 | 2 |
| #23781667 | 2 |
| #23781664 | 2 |
| #23781628 | 2 |
| #428×C163 | 2 |
| #3093 | 163 |