Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
750 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 750 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23774224 | C2 | semidirect |
| 4. #23764385 | C2 | semidirect |
| 5. #23761919 | C2 | semidirect |
| 6. #23761305 | C2 | semidirect |
| 264. C79 | #9935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774224 | 2 |
| #23772660 | 2 |
| #23769129 | 2 |
| #23764385 | 2 |
| #23761919 | 2 |
| #23761305 | 2 |
| C79×#1789 | 2 |
| #9935 | 79 |