Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
422 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 111 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. #19098966 | C4 | semidirect |
| 10. #19098942 | C4 | semidirect |
| 11. #19098915 | C4 | semidirect |
| 12. #19098913 | C4 | semidirect |
| 187. C79 | #9720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773982 | 2 |
| #23764344 | 2 |
| C4×#14579092 | 2 |
| #23761899 | 2 |
| #23761898 | 2 |
| #23761687 | 2 |
| C79×#1986 | 2 |
| #9720 | 79 |