Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23781951 | C2 | semidirect |
| 5. #23781950 | C2 | semidirect |
| 6. #23781872 | C2 | semidirect |
| 8. #23781772 | C2 | semidirect |
| 9. #23781769 | C2 | semidirect |
| 11. #462×C163 | C2 | semidirect |
| 132. C163 | #3113 | semidirect |
| 140. #462 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782220 | 2 |
| C4×Q8×D163 | 2 |
| #23781994 | 2 |
| #23781951 | 2 |
| #23781950 | 2 |
| #23781872 | 2 |
| #23781819 | 2 |
| #23781772 | 2 |
| #23781769 | 2 |
| #23781721 | 2 |
| #462×C163 | 2 |
| #3113 | 163 |