Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
516 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23772035 | C2 | semidirect |
| 3. #23763475 | C2 | semidirect |
| 5. #23761254 | C2 | semidirect |
| 6. #23761252 | C2 | semidirect |
| 16. #19098466 | C4 | semidirect |
| 17. #19098466 | C4 | semidirect |
| 20. #19098432 | C4 | semidirect |
| 21. #19098428 | C4 | semidirect |
| 243. C79 | #9446 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772035 | 2 |
| #23767863 | 2 |
| #23763475 | 2 |
| #23761929 | 2 |
| #23761254 | 2 |
| #23761252 | 2 |
| C79×#1510 | 2 |
| #9446 | 79 |