Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
434 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 16. #501×C79 | C4 | semidirect |
| 111. C79 | #9440 | semidirect |
| 114. #501 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766506 | 2 |
| #23762027 | 2 |
| #23761912 | 2 |
| #23761294 | 2 |
| C79×#3166 | 2 |
| #9440 | 79 |