Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
458 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 1. #23774610 | C2 | semidirect |
| 4. #23761820 | C2 | semidirect |
| 6. #23761271 | C2 | semidirect |
| 7. C79×#1497 | C2 | semidirect |
| 188. #1497 | D79 | semidirect |
| 192. C79 | #10125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774610 | 2 |
| #23774405 | 2 |
| #23773789 | 2 |
| #23761820 | 2 |
| #23761751 | 2 |
| #23761271 | 2 |
| C79×#1497 | 2 |
| #10125 | 79 |