Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
280 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 55 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. #100×D163 | C2 | semidirect |
| 3. #99×D163 | C2 | semidirect |
| 4. #23781456 | C2 | semidirect |
| 5. #23781454 | C2 | semidirect |
| 6. #23781452 | C2 | semidirect |
| 7. AΣL(1,𝔽16)×C163 | C2 | semidirect |
| 8. C22×C22⋊D163 | C4 | semidirect |
| 11. #19104719 | C4 | semidirect |
| 16. #19104704 | C4 | semidirect |
| 19. C22⋊C4×D163 | C4 | semidirect |
| 39. C22×Dic163 | C2×C4 | semidirect |
| 51. C22⋊Dic163 | C2×C4 | semidirect |
| 55. C24×C163 | C2×C4 | semidirect |
| 61. C22⋊C4×C163 | C2×C4 | semidirect |
| 135. C163 | #2121 | semidirect |
| 143. AΣL(1,𝔽16) | D163 | semidirect |
| 165. C24 | C4×D163 | semidirect |
| 197. C22⋊C4 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782225 | 2 |
| #100×D163 | 2 |
| #99×D163 | 2 |
| #23781456 | 2 |
| #23781454 | 2 |
| #23781452 | 2 |
| AΣL(1,𝔽16)×C163 | 2 |
| #2121 | 163 |