Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
722 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 722 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#19098352 | C2 | semidirect |
| 4. #23761517 | C2 | semidirect |
| 7. C2×#14579142 | C4 | semidirect |
| 9. C22×Dic79⋊C4 | C4 | semidirect |
| 15. #19098443 | C4 | semidirect |
| 19. #19098426 | C4 | semidirect |
| 247. C79 | #13081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098547 | 2 |
| #23766731 | 2 |
| C2×#19098352 | 2 |
| #23761517 | 2 |
| C79×#1782 | 2 |
| #13081 | 79 |