Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 420 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. #23782009 | C2 | semidirect |
| 4. #23782000 | C2 | semidirect |
| 5. #23781996 | C2 | semidirect |
| 6. #23781988 | C2 | semidirect |
| 7. #23781976 | C2 | semidirect |
| 8. #23781700 | C2 | semidirect |
| 9. #23781658 | C2 | semidirect |
| 10. C22⋊C8×D163 | C2 | semidirect |
| 11. #481×C163 | C2 | semidirect |
| 30. #19104668 | C22 | semidirect |
| 31. #19104668 | C22 | semidirect |
| 32. #19104667 | C22 | semidirect |
| 33. #19104660 | C22 | semidirect |
| 34. #19104658 | C22 | semidirect |
| 35. #19104656 | C22 | semidirect |
| 40. #106×C163 | C22 | semidirect |
| 41. #102×C163 | C22 | semidirect |
| 143. C163 | #3091 | semidirect |
| 151. #481 | D163 | semidirect |
| 179. #106 | C2×D163 | semidirect |
| 183. #102 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782175 | 2 |
| C2×#19104693 | 2 |
| #23782009 | 2 |
| #23782000 | 2 |
| #23781996 | 2 |
| #23781988 | 2 |
| #23781976 | 2 |
| #23781700 | 2 |
| #23781658 | 2 |
| C22⋊C8×D163 | 2 |
| #481×C163 | 2 |
| #3091 | 163 |