Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
388 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 20. #19098379 | C4 | semidirect |
| 158. C79 | #12941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772268 | 2 |
| #23765186 | 2 |
| C2×#19098379 | 2 |
| #23764183 | 2 |
| #23761496 | 2 |
| #23761488 | 2 |
| C2×#358×C79 | 2 |
| #12941 | 79 |