Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 350 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. #23782385 | C2 | semidirect |
| 2. #23782376 | C2 | semidirect |
| 3. #23782018 | C2 | semidirect |
| 4. #23782017 | C2 | semidirect |
| 5. #23781975 | C2 | semidirect |
| 7. #23781871 | C2 | semidirect |
| 8. #23781789 | C2 | semidirect |
| 9. #23781752 | C2 | semidirect |
| 11. #476×C163 | C2 | semidirect |
| 120. C163 | #3360 | semidirect |
| 127. #476 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782385 | 2 |
| #23782376 | 2 |
| #23782018 | 2 |
| #23782017 | 2 |
| #23781975 | 2 |
| #23781879 | 2 |
| #23781871 | 2 |
| #23781789 | 2 |
| #23781752 | 2 |
| C4×#14579684 | 2 |
| #476×C163 | 2 |
| #3360 | 163 |