Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
616 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 1. C22×#14579684 | C2 | semidirect |
| 2. C22×C8×D163 | C2 | semidirect |
| 3. C2×#19104710 | C2 | semidirect |
| 4. C2×#19104706 | C2 | semidirect |
| 5. #23781900 | C2 | direct (N × H) |
| 6. C2×#19104668 | C2 | semidirect |
| 7. C2×#19104657 | C2 | semidirect |
| 8. C2×#102×C163 | C2 | semidirect |
| 14. C2×#14579684 | C22 | semidirect |
| 17. C2×C8×D163 | C22 | semidirect |
| 19. #19104710 | C22 | semidirect |
| 21. #19104706 | C22 | semidirect |
| 25. #19104668 | C22 | semidirect |
| 26. #19104657 | C22 | semidirect |
| 30. #102×C163 | C22 | semidirect |
| 48. C2×C163⋊C8 | D4 | semidirect |
| 72. C22×D163 | D8 | semidirect |
| 86. C163⋊C8 | C2×D4 | semidirect |
| 117. C2×D163 | C2×D8 | semidirect |
| 125. C2×C163 | #466 | semidirect |
| 131. C163 | C2×#466 | semidirect |
| 140. C2×#102 | D163 | semidirect |
| 162. #102 | C2×D163 | semidirect |
| 259. C2 | #23781900 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579684 | 2 |
| C22×C8×D163 | 2 |
| C2×#19104710 | 2 |
| C2×#19104706 | 2 |
| #23781900 | 2 |
| C2×#19104668 | 2 |
| C2×#19104657 | 2 |
| C2×#102×C163 | 2 |
| C2×#466 | 163 |