Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
714 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 187 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 |
|---|---|---|
| 144. C79 | #23825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579161 | 2 |
| C4×#14579153 | 2 |
| #23764964 | 2 |
| #23764820 | 2 |
| #23764647 | 2 |
| #23764552 | 2 |
| #23763231 | 2 |
| C79×#1745 | 2 |
| #23825 | 79 |