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. #23772418 | C2 | semidirect |
| 3. #23763213 | C2 | semidirect |
| 4. #23761908 | C2 | semidirect |
| 5. #23761294 | C2 | semidirect |
| 6. #23761272 | C2 | semidirect |
| 7. C79×#1525 | C2 | semidirect |
| 10. #19098845 | C4 | semidirect |
| 11. #19098840 | C4 | semidirect |
| 12. #19098760 | C4 | semidirect |
| 13. #19098755 | C4 | semidirect |
| 206. #1525 | 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 |
|---|---|
| #23773545 | 2 |
| #23772418 | 2 |
| #23763213 | 2 |
| #23761908 | 2 |
| #23761294 | 2 |
| #23761272 | 2 |
| C79×#1525 | 2 |
| #9162 | 79 |