Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
590 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 87 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. #23761420 | C2 | semidirect |
| 5. C23×Dic158 | C4 | semidirect |
| 8. #19098483 | C4 | semidirect |
| 13. #19098423 | C4 | semidirect |
| 172. C79 | #11785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766765 | 2 |
| #23761741 | 2 |
| #23761420 | 2 |
| C4×#99×C79 | 2 |
| #11785 | 79 |