Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
274 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #23761513 | C2 | semidirect |
| 5. #23761500 | C2 | semidirect |
| 6. #23761499 | C2 | semidirect |
| 7. C79×#2161 | C2 | semidirect |
| 133. #2161 | D79 | semidirect |
| 140. C79 | #13497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765027 | 2 |
| #23763456 | 2 |
| #23763447 | 2 |
| #23761513 | 2 |
| #23761500 | 2 |
| #23761499 | 2 |
| C79×#2161 | 2 |
| #13497 | 79 |