Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23781681 | C2 | semidirect |
| 3. #23781661 | C2 | semidirect |
| 4. #23781633 | C2 | semidirect |
| 5. #23781436 | C2 | semidirect |
| 6. #23781429 | C2 | semidirect |
| 7. #568×C163 | C2 | semidirect |
| 10. #19104765 | C4 | semidirect |
| 12. #19104760 | C4 | semidirect |
| 118. C163 | #1881 | semidirect |
| 121. #568 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782463 | 2 |
| #23781681 | 2 |
| #23781661 | 2 |
| #23781633 | 2 |
| #23781436 | 2 |
| #23781429 | 2 |
| #568×C163 | 2 |
| #1881 | 163 |