Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
428 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 25. #14579159 | C8 | semidirect |
| 168. C79 | #11478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579159 | 2 |
| #23761724 | 2 |
| #23761345 | 2 |
| #23761333 | 2 |
| C79×#1461 | 2 |
| #11478 | 79 |