Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
438 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 69 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. C2×#19104652 | C2 | semidirect |
| 3. #23781451 | C2 | direct (N × H) |
| 4. C2×#99×C163 | C2 | semidirect |
| 5. C24×D163 | C4 | semidirect |
| 10. #19104703 | C4 | semidirect |
| 12. C2×C22⋊Dic163 | C4 | semidirect |
| 15. #19104652 | C22 | semidirect |
| 19. #99×C163 | C22 | semidirect |
| 25. C23×D163 | C2×C4 | semidirect |
| 34. C22⋊Dic163 | C2×C4 | semidirect |
| 121. C2×C163 | AΣL(1,𝔽16) | semidirect |
| 124. C163 | C2×AΣL(1,𝔽16) | semidirect |
| 128. C2×#99 | D163 | semidirect |
| 144. #99 | C2×D163 | semidirect |
| 247. C2 | #23781451 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104703 | 2 |
| C2×#19104652 | 2 |
| #23781451 | 2 |
| C2×#99×C163 | 2 |
| C2×AΣL(1,𝔽16) | 163 |