Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
510 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. C22×#14579684 | C2 | semidirect |
| 2. C2×#19104656 | C2 | semidirect |
| 3. #23781567 | C2 | semidirect |
| 4. #23781420 | C2 | semidirect |
| 5. C2×#127×C163 | C2 | semidirect |
| 22. C2×D652 | D4 | semidirect |
| 27. C2×C163⋊C8 | D4 | semidirect |
| 66. C2×C4×C163 | D8 | semidirect |
| 97. C163 | #2011 | semidirect |
| 100. C2×#127 | D163 | semidirect |
| 163. C2×C4 | #14579684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579684 | 2 |
| C2×#19104656 | 2 |
| #23781567 | 2 |
| #23781420 | 2 |
| C2×#127×C163 | 2 |
| #2011 | 163 |