Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
348 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23782022 | C2 | semidirect |
| 4. #23781962 | C2 | semidirect |
| 5. #23781947 | C2 | semidirect |
| 6. #23781887 | C2 | semidirect |
| 8. Q8×C163⋊C8 | C2 | semidirect |
| 9. C4×#14579689 | C2 | semidirect |
| 10. C4×#14579686 | C2 | semidirect |
| 11. #557×C163 | C2 | semidirect |
| 117. C163 | #3365 | semidirect |
| 120. #557 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782400 | 2 |
| #23782022 | 2 |
| #23782013 | 2 |
| #23781962 | 2 |
| #23781947 | 2 |
| #23781887 | 2 |
| #23781865 | 2 |
| Q8×C163⋊C8 | 2 |
| C4×#14579689 | 2 |
| C4×#14579686 | 2 |
| #557×C163 | 2 |
| #3365 | 163 |