Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
552 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 185 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. #23781559 | C2 | semidirect |
| 3. #23781559 | C2 | semidirect |
| 4. #23781546 | C2 | semidirect |
| 6. C4×Dic163⋊C4 | C2 | semidirect |
| 7. C22⋊C4×Dic163 | C2 | semidirect |
| 8. C22⋊C4×Dic163 | C2 | semidirect |
| 12. #19104716 | C4 | semidirect |
| 36. C22×Dic163 | C2×C4 | semidirect |
| 42. Dic163⋊C4 | C2×C4 | semidirect |
| 46. C22⋊Dic163 | C2×C4 | semidirect |
| 126. C163 | #2374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104716 | 2 |
| #23781559 | 2 |
| #23781546 | 2 |
| #23781545 | 2 |
| C4×Dic163⋊C4 | 2 |
| C22⋊C4×Dic163 | 2 |
| #390×C163 | 2 |
| #2374 | 163 |