Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
292 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 9. #19098963 | C4 | semidirect |
| 10. #19098941 | C4 | semidirect |
| 14. #19098670 | C4 | semidirect |
| 15. #19098669 | C4 | semidirect |
| 146. C79 | #11771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774054 | 2 |
| #23765213 | 2 |
| #23763156 | 2 |
| #23761393 | 2 |
| #23761389 | 2 |
| #23761388 | 2 |
| C79×#1342 | 2 |
| #11771 | 79 |