Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
560 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 7. #19098330 | C4 | semidirect |
| 9. #19098287 | C4 | semidirect |
| 12. C22×C42×C79 | C4 | semidirect |
| 14. C2×#95×C79 | C4 | semidirect |
| 217. C79 | #7213 | semidirect |
| 220. C22×C42 | Dic79 | semidirect |
| 224. C2×#95 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763474 | 2 |
| #23761727 | 2 |
| C79×#1437 | 2 |
| #7213 | 79 |