Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19104763 | C2 | semidirect |
| 2. C2×#19104743 | C2 | semidirect |
| 3. #23782246 | C2 | semidirect |
| 4. #23782234 | C2 | semidirect |
| 5. #23781919 | C2 | semidirect |
| 6. #23781912 | C2 | semidirect |
| 7. #23781902 | C2 | semidirect |
| 8. #23781895 | C2 | semidirect |
| 9. #23781659 | C2 | semidirect |
| 10. C2×#19104655 | C2 | semidirect |
| 11. #428×C163 | C2 | semidirect |
| 19. C2×#14579682 | C22 | semidirect |
| 21. C2×C8×D163 | C22 | semidirect |
| 25. #19104715 | C22 | semidirect |
| 29. #19104710 | C22 | semidirect |
| 32. #19104658 | C22 | semidirect |
| 33. #19104658 | C22 | semidirect |
| 36. #19104655 | C22 | semidirect |
| 37. #19104655 | C22 | semidirect |
| 41. #107×C163 | C22 | semidirect |
| 42. #106×C163 | C22 | semidirect |
| 77. M16×C163 | D4 | semidirect |
| 151. C163 | #3062 | semidirect |
| 161. #428 | D163 | semidirect |
| 187. #107 | C2×D163 | semidirect |
| 188. #106 | C2×D163 | semidirect |
| 220. M16 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104763 | 2 |
| C2×#19104743 | 2 |
| #23782246 | 2 |
| #23782234 | 2 |
| #23781919 | 2 |
| #23781912 | 2 |
| #23781902 | 2 |
| #23781895 | 2 |
| #23781659 | 2 |
| C2×#19104655 | 2 |
| #428×C163 | 2 |
| #3062 | 163 |