Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19104754 | C2 | semidirect |
| 2. C22×C8×D163 | C2 | semidirect |
| 3. #23782175 | C2 | semidirect |
| 4. #23781907 | C2 | semidirect |
| 5. #23781906 | C2 | semidirect |
| 6. #23781898 | C2 | semidirect |
| 7. #23781893 | C2 | semidirect |
| 8. #23781892 | C2 | semidirect |
| 9. #23781702 | C2 | semidirect |
| 10. #23781658 | C2 | semidirect |
| 11. #466×C163 | C2 | semidirect |
| 15. C2×Dic652 | C22 | semidirect |
| 16. C2×#14579687 | C22 | semidirect |
| 31. #19104669 | C22 | semidirect |
| 32. #19104666 | C22 | semidirect |
| 33. #19104660 | C22 | semidirect |
| 34. #19104658 | C22 | semidirect |
| 35. #19104656 | C22 | semidirect |
| 36. C2×D8×C163 | C22 | semidirect |
| 39. #107×C163 | C22 | semidirect |
| 40. #102×C163 | C22 | semidirect |
| 63. C8×D163 | D4 | semidirect |
| 121. C22×C163 | #135 | semidirect |
| 129. C2×D163 | #135 | semidirect |
| 145. C163 | #3050 | semidirect |
| 153. #466 | D163 | semidirect |
| 163. C2×D8 | C2×D163 | semidirect |
| 181. #107 | C2×D163 | semidirect |
| 186. #102 | C2×D163 | semidirect |
| 274. C22 | #19104754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104754 | 2 |
| C22×C8×D163 | 2 |
| #23782175 | 2 |
| #23781907 | 2 |
| #23781906 | 2 |
| #23781898 | 2 |
| #23781893 | 2 |
| #23781892 | 2 |
| #23781702 | 2 |
| #23781658 | 2 |
| #466×C163 | 2 |
| #3050 | 163 |