Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
530 conjugacy classes of subgroups.
The subgroup lattice has 368 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#19098304 | C2 | semidirect |
| 4. #23761282 | C2 | semidirect |
| 189. C79 | #9126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771710 | 2 |
| #23763162 | 2 |
| C2×#19098304 | 2 |
| #23761282 | 2 |
| C2×#432×C79 | 2 |
| #9126 | 79 |