Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 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. #23782268 | C2 | semidirect |
| 2. #23782066 | C2 | semidirect |
| 3. #23782040 | C2 | semidirect |
| 4. #23782028 | C2 | semidirect |
| 5. #23781916 | C2 | semidirect |
| 6. #23781901 | C2 | semidirect |
| 7. #23781774 | C2 | semidirect |
| 8. D8×Dic163 | C2 | semidirect |
| 9. #23781747 | C2 | semidirect |
| 10. #23781620 | C2 | semidirect |
| 11. #466×C163 | C2 | semidirect |
| 123. C163 | #3176 | semidirect |
| 131. #466 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782268 | 2 |
| #23782066 | 2 |
| #23782040 | 2 |
| #23782028 | 2 |
| #23781916 | 2 |
| #23781901 | 2 |
| #23781774 | 2 |
| D8×Dic163 | 2 |
| #23781747 | 2 |
| #23781620 | 2 |
| #466×C163 | 2 |
| #3176 | 163 |