Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
676 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23768773 | C2 | semidirect |
| 4. C2×#19098293 | C2 | semidirect |
| 5. C79×#1296 | C2 | semidirect |
| 55. C2×Dic158 | SD16 | semidirect |
| 157. #1296 | D79 | semidirect |
| 158. C79 | #10230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098764 | 2 |
| #23768773 | 2 |
| #23764205 | 2 |
| C2×#19098293 | 2 |
| C79×#1296 | 2 |
| #10230 | 79 |