Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
470 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23772058 | C2 | semidirect |
| 5. #23761306 | C2 | semidirect |
| 6. #23761288 | C2 | semidirect |
| 7. C79×#1825 | C2 | semidirect |
| 16. #19098606 | C4 | semidirect |
| 17. #19098606 | C4 | semidirect |
| 19. #19098567 | C4 | semidirect |
| 20. #19098567 | C4 | semidirect |
| 225. #1825 | D79 | semidirect |
| 230. C79 | #9348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773340 | 2 |
| #23772058 | 2 |
| #23761967 | 2 |
| #23761759 | 2 |
| #23761306 | 2 |
| #23761288 | 2 |
| C79×#1825 | 2 |
| #9348 | 79 |