Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
678 conjugacy classes of subgroups.
The subgroup lattice has 520 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. #19098287 | C4 | semidirect |
| 14. #323×C79 | C4 | semidirect |
| 22. C23×Dic79 | C8 | semidirect |
| 27. C2×C22⋊Dic79 | C8 | semidirect |
| 263. C79 | #7187 | semidirect |
| 274. #323 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098287 | 2 |
| #23761622 | 2 |
| C2×#323×C79 | 2 |
| #7187 | 79 |