Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
348 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23782390 | C2 | semidirect |
| 3. #23782021 | C2 | semidirect |
| 5. #23781964 | C2 | semidirect |
| 6. #23781890 | C2 | semidirect |
| 8. #23781789 | C2 | semidirect |
| 9. C4×#14579689 | C2 | semidirect |
| 10. #23781752 | C2 | semidirect |
| 11. #475×C163 | C2 | semidirect |
| 117. C163 | #3365 | semidirect |
| 124. #475 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782400 | 2 |
| #23782390 | 2 |
| #23782021 | 2 |
| #23782013 | 2 |
| #23781964 | 2 |
| #23781890 | 2 |
| #23781866 | 2 |
| #23781789 | 2 |
| C4×#14579689 | 2 |
| #23781752 | 2 |
| #475×C163 | 2 |
| #3365 | 163 |