Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 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×Q8×D163 | C2 | semidirect |
| 2. C2×#19104764 | C2 | semidirect |
| 4. #23781823 | C2 | semidirect |
| 5. #23781822 | C2 | semidirect |
| 6. #23781821 | C2 | semidirect |
| 7. #23781803 | C2 | semidirect |
| 8. #23781802 | C2 | semidirect |
| 9. #23781672 | C2 | semidirect |
| 10. #23781627 | C2 | semidirect |
| 11. #448×C163 | C2 | semidirect |
| 23. C2×Dic652 | C22 | semidirect |
| 24. C2×#14579689 | C22 | semidirect |
| 25. C2×#14579687 | C22 | semidirect |
| 35. #19104660 | C22 | semidirect |
| 36. #19104659 | C22 | semidirect |
| 37. #19104658 | C22 | semidirect |
| 41. C2×SD16×C163 | C22 | semidirect |
| 43. #103×C163 | C22 | semidirect |
| 59. Q8×D163 | D4 | semidirect |
| 144. C22×C163 | #137 | semidirect |
| 152. C2×D163 | #137 | semidirect |
| 169. C163 | #3004 | semidirect |
| 179. #448 | D163 | semidirect |
| 197. C2×SD16 | C2×D163 | semidirect |
| 211. #103 | C2×D163 | semidirect |
| 321. C22 | #19104764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D163 | 2 |
| C2×#19104764 | 2 |
| #23782175 | 2 |
| #23781823 | 2 |
| #23781822 | 2 |
| #23781821 | 2 |
| #23781803 | 2 |
| #23781802 | 2 |
| #23781672 | 2 |
| #23781627 | 2 |
| #448×C163 | 2 |
| #3004 | 163 |