Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
750 conjugacy classes of subgroups.
The subgroup lattice has 598 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #23761522 | C2 | direct (N × H) |
| 297. C2×C79 | #1392 | semidirect |
| 303. C79 | C2×#1392 | semidirect |
| 595. C2 | #23761522 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098547 | 2 |
| C2×#19098530 | 2 |
| #23761522 | 2 |
| C2×#413×C79 | 2 |
| C2×#1392 | 79 |