Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 153. C79 | #11863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773981 | 2 |
| #23765196 | 2 |
| #23763536 | 2 |
| #23761419 | 2 |
| #23761418 | 2 |
| #23761417 | 2 |
| C79×#1350 | 2 |
| #11863 | 79 |