Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 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. C2×#19104760 | C2 | semidirect |
| 2. C2×M16×D163 | C2 | semidirect |
| 3. #23782172 | C2 | semidirect |
| 4. C2×#19104710 | C2 | semidirect |
| 5. #23781917 | C2 | semidirect |
| 6. #23781914 | C2 | semidirect |
| 7. #23781900 | C2 | semidirect |
| 8. #23781897 | C2 | semidirect |
| 9. #23781705 | C2 | semidirect |
| 10. #23781671 | C2 | semidirect |
| 11. #417×C163 | C2 | semidirect |
| 16. C2×#14579686 | C22 | semidirect |
| 17. C2×#14579684 | C22 | semidirect |
| 19. C2×#14579682 | C22 | semidirect |
| 21. C2×C8×D163 | C22 | semidirect |
| 23. #19104711 | C22 | semidirect |
| 24. #19104711 | C22 | semidirect |
| 29. #19104706 | C22 | semidirect |
| 30. #19104706 | C22 | semidirect |
| 36. #19104668 | C22 | semidirect |
| 37. #19104666 | C22 | semidirect |
| 38. #19104657 | C22 | semidirect |
| 39. #19104657 | C22 | semidirect |
| 43. #103×C163 | C22 | semidirect |
| 44. #102×C163 | C22 | semidirect |
| 65. #14579683 | D4 | semidirect |
| 120. C163⋊C8 | C2×D4 | semidirect |
| 154. C2×D163 | AGL(1,ℤ/8) | semidirect |
| 172. C163 | #3055 | semidirect |
| 184. #417 | D163 | semidirect |
| 214. #103 | C2×D163 | semidirect |
| 217. #102 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104760 | 2 |
| C2×M16×D163 | 2 |
| #23782172 | 2 |
| C2×#19104710 | 2 |
| #23781917 | 2 |
| #23781914 | 2 |
| #23781900 | 2 |
| #23781897 | 2 |
| #23781705 | 2 |
| #23781671 | 2 |
| #417×C163 | 2 |
| #3055 | 163 |