Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
380 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 85 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. #19098959 | C4 | semidirect |
| 10. #19098942 | C4 | semidirect |
| 11. #19098915 | C4 | semidirect |
| 12. #19098913 | C4 | semidirect |
| 155. C79 | #9416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774141 | 2 |
| #23772505 | 2 |
| #23761952 | 2 |
| #23761951 | 2 |
| #23761271 | 2 |
| #23761266 | 2 |
| C79×#1537 | 2 |
| #9416 | 79 |