Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23782220 | C2 | semidirect |
| 3. #23782004 | C2 | semidirect |
| 4. #23781960 | C2 | semidirect |
| 5. #23781956 | C2 | semidirect |
| 6. #23781867 | C2 | semidirect |
| 8. #23781772 | C2 | semidirect |
| 9. #23781768 | C2 | semidirect |
| 10. #23781721 | C2 | semidirect |
| 11. #462×C163 | C2 | semidirect |
| 136. C163 | #3116 | semidirect |
| 143. #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×#14579700 | 2 |
| #23782004 | 2 |
| #23781960 | 2 |
| #23781956 | 2 |
| #23781867 | 2 |
| #23781826 | 2 |
| #23781772 | 2 |
| #23781768 | 2 |
| #23781721 | 2 |
| #462×C163 | 2 |
| #3116 | 163 |