Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
340 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 1. #23782390 | C2 | semidirect |
| 3. #23782032 | C2 | semidirect |
| 4. #23781970 | C2 | semidirect |
| 5. #23781957 | C2 | semidirect |
| 8. #23781795 | C2 | semidirect |
| 11. #487×C163 | C2 | semidirect |
| 116. C163 | #3372 | semidirect |
| 121. #487 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782390 | 2 |
| #23782376 | 2 |
| #23782032 | 2 |
| #23781970 | 2 |
| #23781957 | 2 |
| #23781869 | 2 |
| #23781867 | 2 |
| #23781795 | 2 |
| #23781768 | 2 |
| C4×#14579688 | 2 |
| #487×C163 | 2 |
| #3372 | 163 |