Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
930 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 203 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 |
|---|---|---|
| 1. C2×#19098345 | C2 | semidirect |
| 2. #23765011 | C2 | semidirect |
| 130. C79 | #12682 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098345 | 2 |
| #23765011 | 2 |
| C22×#131×C79 | 2 |
| #12682 | 79 |