Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
286 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 81 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. #23781629 | C2 | semidirect |
| 2. #23781525 | C2 | semidirect |
| 3. #23781402 | C2 | semidirect |
| 4. #23781399 | C2 | semidirect |
| 12. C2×#41×C163 | C4 | semidirect |
| 15. C22⋊Q8×C163 | C4 | semidirect |
| 17. #121×C163 | C4 | semidirect |
| 22. #117×C163 | C4 | semidirect |
| 117. C163 | #1513 | semidirect |
| 124. C2×#41 | Dic163 | semidirect |
| 128. C22⋊Q8 | Dic163 | semidirect |
| 130. #121 | Dic163 | semidirect |
| 135. #117 | Dic163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781629 | 2 |
| #23781525 | 2 |
| #23781402 | 2 |
| #23781399 | 2 |
| #525×C163 | 2 |
| #1513 | 163 |