Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1050 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 143 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. #23762069 | C2 | semidirect |
| 3. #23761824 | C2 | semidirect |
| 4. #23761724 | C2 | semidirect |
| 5. C79×#1801 | C2 | semidirect |
| 190. #1801 | D79 | semidirect |
| 194. C79 | #8384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099235 | 2 |
| #23762069 | 2 |
| #23761824 | 2 |
| #23761724 | 2 |
| C79×#1801 | 2 |
| #8384 | 79 |