Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
334 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 334 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 |
|---|---|---|
| 9. #19098967 | C4 | semidirect |
| 10. #19098941 | C4 | semidirect |
| 14. Q16×Dic79 | C4 | semidirect |
| 15. #19098657 | C4 | semidirect |
| 164. C79 | #11857 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773981 | 2 |
| #23765196 | 2 |
| #23763526 | 2 |
| #23761413 | 2 |
| #23761412 | 2 |
| #23761411 | 2 |
| C79×#1348 | 2 |
| #11857 | 79 |