Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
570 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 3. #23761971 | C2 | semidirect |
| 4. #23761278 | C2 | semidirect |
| 11. #19098502 | C4 | semidirect |
| 12. #19098499 | C4 | semidirect |
| 13. #19098483 | C4 | semidirect |
| 14. #19098475 | C4 | semidirect |
| 199. C79 | #9383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772424 | 2 |
| #23768576 | 2 |
| #23761971 | 2 |
| #23761278 | 2 |
| C79×#1799 | 2 |
| #9383 | 79 |