Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
470 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 105 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. #23772483 | C2 | semidirect |
| 3. #23763416 | C2 | semidirect |
| 6. #23761260 | C2 | semidirect |
| 7. C79×#1301 | C2 | semidirect |
| 12. #19098774 | C4 | semidirect |
| 13. #19098764 | C4 | semidirect |
| 189. #1301 | D79 | semidirect |
| 191. C79 | #9310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772874 | 2 |
| #23772483 | 2 |
| #23763416 | 2 |
| #23761961 | 2 |
| #23761798 | 2 |
| #23761260 | 2 |
| C79×#1301 | 2 |
| #9310 | 79 |