Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
406 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 156. C79 | #9861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773910 | 2 |
| #23763571 | 2 |
| #23761856 | 2 |
| #23761855 | 2 |
| #23761854 | 2 |
| C2×#19098285 | 2 |
| C79×#1493 | 2 |
| #9861 | 79 |