Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
438 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. #23761932 | C2 | semidirect |
| 4. #23761763 | C2 | semidirect |
| 5. #23761308 | C2 | semidirect |
| 6. #23761277 | C2 | semidirect |
| 10. #19098896 | C4 | semidirect |
| 11. #19098879 | C4 | semidirect |
| 15. #19098718 | C4 | semidirect |
| 16. #19098701 | C4 | semidirect |
| 224. C79 | #9331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774226 | 2 |
| #23772462 | 2 |
| #23761932 | 2 |
| #23761763 | 2 |
| #23761308 | 2 |
| #23761277 | 2 |
| C79×#1516 | 2 |
| #9331 | 79 |