Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
432 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 6. C22×Dic316 | C4 | semidirect |
| 13. #19098601 | C4 | semidirect |
| 14. #19098573 | C4 | semidirect |
| 165. C79 | #13233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773055 | 2 |
| #23765094 | 2 |
| #23765053 | 2 |
| #23763450 | 2 |
| C79×#1757 | 2 |
| #13233 | 79 |