Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
792 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 229 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. C22×C8×D163 | C2 | semidirect |
| 3. C2×#19104693 | C2 | semidirect |
| 4. #23781658 | C2 | direct (N × H) |
| 5. C2×#19104660 | C2 | semidirect |
| 6. C2×#19104658 | C2 | semidirect |
| 7. C2×#19104656 | C2 | semidirect |
| 8. C2×#102×C163 | C2 | semidirect |
| 11. C2×#14579698 | C4 | semidirect |
| 19. C2×C8×D163 | C22 | semidirect |
| 21. #19104693 | C22 | semidirect |
| 25. #19104660 | C22 | semidirect |
| 26. #19104658 | C22 | semidirect |
| 27. #19104656 | C22 | semidirect |
| 31. #102×C163 | C22 | semidirect |
| 35. #14579698 | C2×C4 | semidirect |
| 123. C2×C163 | #416 | semidirect |
| 128. C163 | C2×#416 | semidirect |
| 137. C2×#102 | D163 | semidirect |
| 160. #102 | C2×D163 | semidirect |
| 253. C2 | #23781658 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579698 | 2 |
| C22×C8×D163 | 2 |
| C2×#19104693 | 2 |
| #23781658 | 2 |
| C2×#19104660 | 2 |
| C2×#19104658 | 2 |
| C2×#19104656 | 2 |
| C2×#102×C163 | 2 |
| C2×#416 | 163 |