Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
492 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 492 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. #23782213 | C2 | semidirect |
| 2. C4×D4×D163 | C2 | semidirect |
| 3. #23781977 | C2 | semidirect |
| 4. #23781946 | C2 | semidirect |
| 5. #23781945 | C2 | semidirect |
| 6. #23781857 | C2 | semidirect |
| 7. #23781797 | C2 | semidirect |
| 8. D8×Dic163 | C2 | semidirect |
| 9. #23781745 | C2 | semidirect |
| 10. #23781717 | C2 | semidirect |
| 11. #459×C163 | C2 | semidirect |
| 16. #19104735 | C22 | semidirect |
| 23. D4×Dic163 | C22 | semidirect |
| 30. #19104669 | C22 | semidirect |
| 31. #19104668 | C22 | semidirect |
| 32. C4⋊(C163⋊C8) | C22 | semidirect |
| 35. #19104656 | C22 | semidirect |
| 37. C8×Dic163 | C22 | semidirect |
| 39. #127×C163 | C22 | semidirect |
| 41. C4⋊C8×C163 | C22 | semidirect |
| 42. #102×C163 | C22 | semidirect |
| 91. D652 | #41 | semidirect |
| 107. C4×D163 | D8 | semidirect |
| 116. D4×C163 | #41 | semidirect |
| 154. C163 | #3100 | semidirect |
| 162. #459 | D163 | semidirect |
| 173. #127 | C2×D163 | semidirect |
| 191. C4⋊C8 | C2×D163 | semidirect |
| 195. #102 | C2×D163 | semidirect |
| 256. D4 | #14579698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782213 | 2 |
| C4×D4×D163 | 2 |
| #23781977 | 2 |
| #23781946 | 2 |
| #23781945 | 2 |
| #23781857 | 2 |
| #23781797 | 2 |
| D8×Dic163 | 2 |
| #23781745 | 2 |
| #23781717 | 2 |
| #459×C163 | 2 |
| #3100 | 163 |