Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
306 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #23781426 | C2 | semidirect |
| 5. #23781425 | C2 | semidirect |
| 6. #23781424 | C2 | semidirect |
| 7. #339×C163 | C2 | semidirect |
| 11. #19104693 | C4 | semidirect |
| 12. #19104693 | C4 | semidirect |
| 15. C4⋊C4×D163 | C4 | semidirect |
| 16. C4⋊C4×D163 | C4 | semidirect |
| 138. C163 | #1826 | semidirect |
| 146. #339 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #117×D163 | 2 |
| #23781628 | 2 |
| C4×(C2×D163)⋊C4 | 2 |
| #23781426 | 2 |
| #23781425 | 2 |
| #23781424 | 2 |
| #339×C163 | 2 |
| #1826 | 163 |