Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. C2×#19104700 | C2 | semidirect |
| 4. #23781971 | C2 | semidirect |
| 5. #23781890 | C2 | semidirect |
| 6. #23781820 | C2 | semidirect |
| 8. #23781769 | C2 | semidirect |
| 9. #23781764 | C2 | semidirect |
| 10. #23781719 | C2 | semidirect |
| 11. #484×C163 | C2 | semidirect |
| 131. C163 | #3117 | semidirect |
| 135. #484 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782201 | 2 |
| C2×#19104700 | 2 |
| #23781983 | 2 |
| #23781971 | 2 |
| #23781890 | 2 |
| #23781820 | 2 |
| #23781806 | 2 |
| #23781769 | 2 |
| #23781764 | 2 |
| #23781719 | 2 |
| #484×C163 | 2 |
| #3117 | 163 |