Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
330 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 330 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 |
|---|---|---|
| 1. #23763554 | C2 | semidirect |
| 3. #23761295 | C2 | semidirect |
| 4. #23761229 | C2 | semidirect |
| 122. C79 | #10627 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763554 | 2 |
| #23762049 | 2 |
| #23761295 | 2 |
| #23761229 | 2 |
| C79×#1963 | 2 |
| #10627 | 79 |