Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
448 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23765094 | C2 | semidirect |
| 4. #23765055 | C2 | semidirect |
| 6. #23763200 | C2 | semidirect |
| 7. C79×#1813 | C2 | semidirect |
| 8. C22×#11929613 | C4 | semidirect |
| 15. #19098601 | C4 | semidirect |
| 16. #19098573 | C4 | semidirect |
| 17. #19098569 | C4 | semidirect |
| 216. #1813 | D79 | semidirect |
| 218. C79 | #13232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773039 | 2 |
| #23765094 | 2 |
| #23765091 | 2 |
| #23765055 | 2 |
| #23765051 | 2 |
| #23763200 | 2 |
| C79×#1813 | 2 |
| #13232 | 79 |