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. #23781455 | C2 | semidirect |
| 5. #23781453 | C2 | semidirect |
| 6. #23781451 | C2 | semidirect |
| 7. #352×C163 | C2 | semidirect |
| 8. C22×D652 | C4 | semidirect |
| 12. #19104718 | C4 | semidirect |
| 16. #19104705 | C4 | semidirect |
| 19. C22⋊C4×D163 | C4 | semidirect |
| 28. C23×D163 | C2×C4 | semidirect |
| 49. C22⋊Dic163 | C2×C4 | semidirect |
| 56. C22×C4×C163 | C2×C4 | semidirect |
| 61. C22⋊C4×C163 | C2×C4 | semidirect |
| 135. C163 | #2121 | semidirect |
| 141. #352 | D163 | semidirect |
| 181. C22×C4 | 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 |
|---|---|
| #23782226 | 2 |
| #100×D163 | 2 |
| #99×D163 | 2 |
| #23781455 | 2 |
| #23781453 | 2 |
| #23781451 | 2 |
| #352×C163 | 2 |
| #2121 | 163 |