Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
396 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23761419 | C2 | semidirect |
| 146. C79 | #11892 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098804 | 2 |
| #23763438 | 2 |
| #23761419 | 2 |
| C2×C22⋊C16×C79 | 2 |
| #11892 | 79 |