Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
566 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. #23761527 | C2 | semidirect |
| 4. #23761526 | C2 | semidirect |
| 5. C79×#1394 | C2 | semidirect |
| 172. #1394 | D79 | semidirect |
| 173. C79 | #12862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765983 | 2 |
| #23763322 | 2 |
| #23761527 | 2 |
| #23761526 | 2 |
| C79×#1394 | 2 |
| #12862 | 79 |