Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×M16×D163 | C2 | semidirect |
| 3. #23782175 | C2 | semidirect |
| 4. #23781924 | C2 | semidirect |
| 5. #23781923 | C2 | semidirect |
| 6. #23781915 | C2 | semidirect |
| 7. #23781910 | C2 | semidirect |
| 8. #23781909 | C2 | semidirect |
| 9. #23781700 | C2 | semidirect |
| 10. #23781658 | C2 | semidirect |
| 11. #469×C163 | C2 | semidirect |
| 15. C2×Dic652 | C22 | semidirect |
| 16. C2×#14579687 | C22 | semidirect |
| 31. #19104668 | C22 | semidirect |
| 32. #19104667 | C22 | semidirect |
| 33. #19104660 | C22 | semidirect |
| 34. #19104658 | C22 | semidirect |
| 35. #19104656 | C22 | semidirect |
| 36. C2×D8×C163 | C22 | semidirect |
| 39. #106×C163 | C22 | semidirect |
| 40. #102×C163 | C22 | semidirect |
| 63. C8×D163 | D4 | semidirect |
| 140. C163 | #3054 | semidirect |
| 148. #469 | D163 | semidirect |
| 158. C2×D8 | C2×D163 | semidirect |
| 177. #106 | C2×D163 | semidirect |
| 181. #102 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104754 | 2 |
| C2×M16×D163 | 2 |
| #23782175 | 2 |
| #23781924 | 2 |
| #23781923 | 2 |
| #23781915 | 2 |
| #23781910 | 2 |
| #23781909 | 2 |
| #23781700 | 2 |
| #23781658 | 2 |
| #469×C163 | 2 |
| #3054 | 163 |