Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
380 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 10. #19098961 | C4 | semidirect |
| 11. #19098943 | C4 | semidirect |
| 12. #19098914 | C4 | semidirect |
| 13. #19098914 | C4 | semidirect |
| 155. C79 | #9416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774145 | 2 |
| #23772505 | 2 |
| #23762037 | 2 |
| #23761952 | 2 |
| #23761265 | 2 |
| C79×#1291 | 2 |
| #9416 | 79 |