Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
458 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 55 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. #23762425 | C2 | semidirect |
| 3. #23762391 | C2 | semidirect |
| 4. #23761423 | C2 | semidirect |
| 5. #23761399 | C2 | semidirect |
| 212. C79 | #12268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23770441 | 2 |
| #23762425 | 2 |
| #23762391 | 2 |
| #23761423 | 2 |
| #23761399 | 2 |
| #23761328 | 2 |
| C79×#2029 | 2 |
| #12268 | 79 |