Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
650 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #23765054 | C2 | semidirect |
| 5. #23761530 | C2 | semidirect |
| 6. #23761522 | C2 | semidirect |
| 7. C79×#2135 | C2 | semidirect |
| 9. C2×#14579192 | C4 | semidirect |
| 10. C22×#11929611 | C4 | semidirect |
| 18. #19098567 | C4 | semidirect |
| 19. #19098557 | C4 | semidirect |
| 251. #2135 | D79 | semidirect |
| 256. C79 | #13097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772675 | 2 |
| #23771877 | 2 |
| #23765054 | 2 |
| #23763371 | 2 |
| #23761530 | 2 |
| #23761522 | 2 |
| C79×#2135 | 2 |
| #13097 | 79 |