Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
764 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23763392 | C2 | semidirect |
| 2. #23761718 | C2 | semidirect |
| 3. #23761403 | C2 | semidirect |
| 8. #19098332 | C22 | semidirect |
| 9. #19098289 | C22 | semidirect |
| 200. C79 | #11880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763392 | 2 |
| #23761718 | 2 |
| #23761403 | 2 |
| C79×#2408 | 2 |
| #11880 | 79 |