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. #23782005 | C2 | semidirect |
| 4. #23782004 | C2 | semidirect |
| 5. #23781988 | C2 | semidirect |
| 6. #23781987 | C2 | semidirect |
| 7. #23781707 | C2 | semidirect |
| 8. #23781705 | C2 | semidirect |
| 9. #23781666 | C2 | semidirect |
| 10. #23781628 | C2 | semidirect |
| 11. #417×C163 | C2 | semidirect |
| 30. #19104669 | C22 | semidirect |
| 31. #19104668 | C22 | semidirect |
| 32. #19104667 | C22 | semidirect |
| 33. #19104666 | C22 | semidirect |
| 34. #19104659 | C22 | semidirect |
| 35. #19104656 | C22 | semidirect |
| 41. #103×C163 | C22 | semidirect |
| 42. #102×C163 | C22 | semidirect |
| 152. C163 | #3093 | semidirect |
| 163. #417 | D163 | semidirect |
| 191. #103 | C2×D163 | semidirect |
| 193. #102 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782172 | 2 |
| C2×#19104693 | 2 |
| #23782005 | 2 |
| #23782004 | 2 |
| #23781988 | 2 |
| #23781987 | 2 |
| #23781707 | 2 |
| #23781705 | 2 |
| #23781666 | 2 |
| #23781628 | 2 |
| #417×C163 | 2 |
| #3093 | 163 |