Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1038 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1038 conjugacy classes of subgroups — too many to draw. Only its 167 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 |
|---|---|---|
| 2. C2×#19098344 | C2 | semidirect |
| 3. #23765011 | C2 | semidirect |
| 4. C79×#2112 | C2 | semidirect |
| 12. C2×#14579101 | C22 | semidirect |
| 16. C2×M32×C79 | C22 | semidirect |
| 128. C22×C79 | #349 | semidirect |
| 150. #2112 | D79 | semidirect |
| 151. C79 | #12681 | semidirect |
| 161. C2×M32 | C2×D79 | semidirect |
| 280. C22 | #19098344 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11929607 | 2 |
| C2×#19098344 | 2 |
| #23765011 | 2 |
| C79×#2112 | 2 |
| #12681 | 79 |