Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
970 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 970 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. #23773531 | C2 | semidirect |
| 4. #23762393 | C2 | semidirect |
| 5. #23762359 | C2 | semidirect |
| 6. #23761913 | C2 | semidirect |
| 193. C79 | #18181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777203 | 2 |
| #23773531 | 2 |
| #23766684 | 2 |
| #23762393 | 2 |
| #23762359 | 2 |
| #23761913 | 2 |
| C79×#1466 | 2 |
| #18181 | 79 |