Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
472 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 2. #23772417 | C2 | semidirect |
| 3. #23763213 | C2 | semidirect |
| 4. #23761991 | C2 | semidirect |
| 5. #23761909 | C2 | semidirect |
| 6. #23761292 | C2 | semidirect |
| 7. C79×#1291 | C2 | semidirect |
| 11. #19098849 | C4 | semidirect |
| 12. #19098844 | C4 | semidirect |
| 13. #19098764 | C4 | semidirect |
| 14. #19098759 | C4 | semidirect |
| 209. #1291 | D79 | semidirect |
| 210. C79 | #9162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773552 | 2 |
| #23772417 | 2 |
| #23763213 | 2 |
| #23761991 | 2 |
| #23761909 | 2 |
| #23761292 | 2 |
| C79×#1291 | 2 |
| #9162 | 79 |