Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23782270 | C2 | semidirect |
| 2. #23781965 | C2 | semidirect |
| 3. #23781962 | C2 | semidirect |
| 4. #23781916 | C2 | semidirect |
| 5. #23781899 | C2 | semidirect |
| 6. #23781860 | C2 | semidirect |
| 7. #23781857 | C2 | semidirect |
| 8. #23781692 | C2 | semidirect |
| 9. #540×C163 | C2 | semidirect |
| 106. C163 | #3259 | semidirect |
| 109. #540 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782270 | 2 |
| #23781965 | 2 |
| #23781962 | 2 |
| #23781916 | 2 |
| #23781899 | 2 |
| #23781860 | 2 |
| #23781857 | 2 |
| #23781692 | 2 |
| #540×C163 | 2 |
| #3259 | 163 |