Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
766 conjugacy classes of subgroups.
The subgroup lattice has 602 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #23761528 | C2 | direct (N × H) |
| 6. C22×#11929608 | C4 | semidirect |
| 7. C23×C79⋊C8 | C4 | semidirect |
| 10. #19098547 | C4 | semidirect |
| 12. C2×#14579080 | C4 | semidirect |
| 16. #19098530 | C4 | semidirect |
| 37. C2×#11929608 | C2×C4 | semidirect |
| 44. C22×C79⋊C8 | C2×C4 | semidirect |
| 46. #14579080 | C2×C4 | semidirect |
| 299. C2×C79 | #1395 | semidirect |
| 305. C79 | C2×#1395 | semidirect |
| 599. C2 | #23761528 | 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 |
| #23761528 | 2 |
| C2×#410×C79 | 2 |
| C2×#1395 | 79 |