Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
354 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 354 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. #23782372 | C2 | semidirect |
| 3. #23782070 | C2 | semidirect |
| 4. #23782007 | C2 | semidirect |
| 5. #23781979 | C2 | semidirect |
| 6. #23781961 | C2 | semidirect |
| 7. #23781956 | C2 | semidirect |
| 8. #23781911 | C2 | semidirect |
| 9. C4×#14579688 | C2 | semidirect |
| 10. #23781707 | C2 | semidirect |
| 11. #436×C163 | C2 | semidirect |
| 121. C163 | #3357 | semidirect |
| 132. #436 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782380 | 2 |
| #23782372 | 2 |
| #23782070 | 2 |
| #23782007 | 2 |
| #23781979 | 2 |
| #23781961 | 2 |
| #23781956 | 2 |
| #23781911 | 2 |
| C4×#14579688 | 2 |
| #23781707 | 2 |
| #436×C163 | 2 |
| #3357 | 163 |