Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
518 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23773344 | C2 | semidirect |
| 3. #23763469 | C2 | semidirect |
| 4. #23761764 | C2 | semidirect |
| 6. #23761277 | C2 | semidirect |
| 211. C79 | #9978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773344 | 2 |
| #23773336 | 2 |
| #23763469 | 2 |
| #23761764 | 2 |
| #23761760 | 2 |
| #23761277 | 2 |
| C79×#3187 | 2 |
| #9978 | 79 |