Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
586 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 15. #391×C79 | C4 | semidirect |
| 16. #389×C79 | C4 | semidirect |
| 156. C79 | #9153 | semidirect |
| 160. #391 | Dic79 | semidirect |
| 161. #389 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098431 | 2 |
| #23763468 | 2 |
| C2×#19098300 | 2 |
| #23761278 | 2 |
| C79×#2855 | 2 |
| #9153 | 79 |