Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
826 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 2. C2×#19098305 | C2 | semidirect |
| 90. C22×C79 | #330 | semidirect |
| 111. C79 | #8335 | semidirect |
| 198. C22 | #19098305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763162 | 2 |
| C2×#19098305 | 2 |
| C22×#125×C79 | 2 |
| #8335 | 79 |