Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
530 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23761921 | C2 | semidirect |
| 4. #23761254 | C2 | semidirect |
| 8. #19098493 | C4 | semidirect |
| 10. #19098488 | C4 | semidirect |
| 11. #19098483 | C4 | semidirect |
| 13. #19098475 | C4 | semidirect |
| 190. C79 | #9184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769317 | 2 |
| C4×#14579076 | 2 |
| #23761921 | 2 |
| #23761254 | 2 |
| C79×#2975 | 2 |
| #9184 | 79 |