Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
972 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 972 conjugacy classes of subgroups — too many to draw. Only its 271 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 |
|---|---|---|
| 1. C2×#19098612 | C2 | semidirect |
| 3. #23764917 | C2 | semidirect |
| 4. C2×#338×C79 | C2 | semidirect |
| 116. C2×#338 | D79 | semidirect |
| 117. C79 | #23723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098612 | 2 |
| #23771844 | 2 |
| #23764917 | 2 |
| C2×#338×C79 | 2 |
| #23723 | 79 |