Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
786 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 3. #23761242 | C2 | semidirect |
| 147. C79 | #8702 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098426 | 2 |
| #23763310 | 2 |
| #23761242 | 2 |
| C79×#1779 | 2 |
| #8702 | 79 |