Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
414 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23763538 | C2 | semidirect |
| 4. #23761275 | C2 | semidirect |
| 5. C2×#334×C79 | C2 | semidirect |
| 136. C2×#334 | D79 | semidirect |
| 139. C79 | #8686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772113 | 2 |
| #23763538 | 2 |
| #23762075 | 2 |
| #23761275 | 2 |
| C2×#334×C79 | 2 |
| #8686 | 79 |