Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
326 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 73 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. #23781528 | C2 | semidirect |
| 3. #23781400 | C2 | semidirect |
| 4. #407×C163 | C2 | semidirect |
| 5. C22×D652 | C4 | semidirect |
| 9. #19104709 | C4 | semidirect |
| 11. C2×C4⋊Dic163 | C4 | semidirect |
| 15. C163⋊#95 | C22 | semidirect |
| 19. C22⋊C8×C163 | C22 | semidirect |
| 102. C163 | #1510 | semidirect |
| 105. #407 | D163 | semidirect |
| 120. C22⋊C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104709 | 2 |
| #23781528 | 2 |
| #23781400 | 2 |
| #407×C163 | 2 |
| #1510 | 163 |