Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
470 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 189. C79 | #10025 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773952 | 2 |
| #23773531 | 2 |
| #23769279 | 2 |
| #23762026 | 2 |
| #23761950 | 2 |
| #23761848 | 2 |
| C79×#1288 | 2 |
| #10025 | 79 |