Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
438 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 438 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 |
|---|---|---|
| 4. #23761933 | C2 | semidirect |
| 5. #23761309 | C2 | semidirect |
| 6. #23761277 | C2 | semidirect |
| 7. C79×#1472 | C2 | semidirect |
| 10. #19098898 | C4 | semidirect |
| 11. #19098881 | C4 | semidirect |
| 15. #19098719 | C4 | semidirect |
| 16. #19098702 | C4 | semidirect |
| 221. #1472 | D79 | semidirect |
| 224. C79 | #9331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774230 | 2 |
| #23772460 | 2 |
| #23761957 | 2 |
| #23761933 | 2 |
| #23761309 | 2 |
| #23761277 | 2 |
| C79×#1472 | 2 |
| #9331 | 79 |