Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
458 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23772487 | C2 | semidirect |
| 3. #23763231 | C2 | semidirect |
| 6. #23761257 | C2 | semidirect |
| 7. C79×#1302 | C2 | semidirect |
| 11. #19098859 | C4 | semidirect |
| 12. #19098859 | C4 | semidirect |
| 13. #19098764 | C4 | semidirect |
| 14. #19098764 | C4 | semidirect |
| 209. #1302 | D79 | semidirect |
| 211. C79 | #9164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773523 | 2 |
| #23772487 | 2 |
| #23763231 | 2 |
| #23762010 | 2 |
| #23761896 | 2 |
| #23761257 | 2 |
| C79×#1302 | 2 |
| #9164 | 79 |