Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
462 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23781991 | C2 | semidirect |
| 4. #23781987 | C2 | semidirect |
| 5. #23781983 | C2 | semidirect |
| 6. #23781979 | C2 | semidirect |
| 7. #23781976 | C2 | semidirect |
| 8. #23781704 | C2 | semidirect |
| 9. #23781668 | C2 | semidirect |
| 10. #23781627 | C2 | semidirect |
| 11. #481×C163 | C2 | semidirect |
| 24. #19104693 | C22 | semidirect |
| 25. C2×C4⋊Dic163 | C22 | semidirect |
| 30. #19104669 | C22 | semidirect |
| 31. #19104668 | C22 | semidirect |
| 32. #19104666 | C22 | semidirect |
| 33. #19104657 | C22 | semidirect |
| 34. #19104656 | C22 | semidirect |
| 35. #19104655 | C22 | semidirect |
| 36. C22⋊(C163⋊C8) | C22 | semidirect |
| 37. (C2×D163)⋊C8 | C22 | semidirect |
| 39. C2×C4⋊C4×C163 | C22 | semidirect |
| 40. #106×C163 | C22 | semidirect |
| 41. #102×C163 | C22 | semidirect |
| 42. C22⋊C8×C163 | C22 | semidirect |
| 153. C163 | #3094 | semidirect |
| 160. #481 | D163 | semidirect |
| 182. C2×C4⋊C4 | C2×D163 | semidirect |
| 189. #106 | C2×D163 | semidirect |
| 193. #102 | C2×D163 | semidirect |
| 196. C22⋊C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #121×D163 | 2 |
| C2×#19104693 | 2 |
| #23781991 | 2 |
| #23781987 | 2 |
| #23781983 | 2 |
| #23781979 | 2 |
| #23781976 | 2 |
| #23781704 | 2 |
| #23781668 | 2 |
| #23781627 | 2 |
| #481×C163 | 2 |
| #3094 | 163 |