Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
756 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 209 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 |
|---|---|---|
| 2. #23782431 | C2 | semidirect |
| 3. #23781649 | C2 | semidirect |
| 4. #23781648 | C2 | semidirect |
| 5. C2×#19104651 | C2 | semidirect |
| 6. #100×D163 | C2 | semidirect |
| 7. #413×C163 | C2 | semidirect |
| 19. C2×#14579683 | C22 | semidirect |
| 20. M16×D163 | C22 | semidirect |
| 21. #19104654 | C22 | semidirect |
| 22. #19104652 | C22 | semidirect |
| 23. #19104651 | C22 | semidirect |
| 25. C2×M16×C163 | C22 | semidirect |
| 26. #101×C163 | C22 | semidirect |
| 27. #100×C163 | C22 | semidirect |
| 120. C163 | #2888 | semidirect |
| 126. #413 | D163 | semidirect |
| 143. C2×M16 | C2×D163 | semidirect |
| 145. #101 | C2×D163 | semidirect |
| 148. #100 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104781 | 2 |
| #23782431 | 2 |
| #23781649 | 2 |
| #23781648 | 2 |
| C2×#19104651 | 2 |
| #100×D163 | 2 |
| #413×C163 | 2 |
| #2888 | 163 |