Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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. C22×#14579688 | C2 | semidirect |
| 2. C2×#19104741 | C2 | semidirect |
| 3. #23782241 | C2 | semidirect |
| 5. #23781912 | C2 | semidirect |
| 6. #23781895 | C2 | semidirect |
| 7. #23781673 | C2 | semidirect |
| 8. #23781669 | C2 | semidirect |
| 9. #427×C163 | C2 | semidirect |
| 18. C2×#14579682 | C22 | semidirect |
| 19. C2×C8×D163 | C22 | semidirect |
| 25. #19104715 | C22 | semidirect |
| 28. #19104658 | C22 | semidirect |
| 33. #107×C163 | C22 | semidirect |
| 34. #106×C163 | C22 | semidirect |
| 62. C2×C8×C163 | D4 | semidirect |
| 120. C163 | #3057 | semidirect |
| 128. #427 | D163 | semidirect |
| 152. #107 | C2×D163 | semidirect |
| 153. #106 | C2×D163 | semidirect |
| 180. C2×C8 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579688 | 2 |
| C2×#19104741 | 2 |
| #23782241 | 2 |
| #23782234 | 2 |
| #23781912 | 2 |
| #23781895 | 2 |
| #23781673 | 2 |
| #23781669 | 2 |
| #427×C163 | 2 |
| #3057 | 163 |