Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
320 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 67 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. #23765075 | C2 | semidirect |
| 3. #23761576 | C2 | semidirect |
| 4. #23761558 | C2 | semidirect |
| 5. C79×#2133 | C2 | semidirect |
| 6. #19099168 | C4 | semidirect |
| 8. #19098937 | C4 | semidirect |
| 9. #19098931 | C4 | semidirect |
| 15. #19098624 | C4 | semidirect |
| 150. #2133 | D79 | semidirect |
| 154. C79 | #13606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774461 | 2 |
| #23765075 | 2 |
| #23761576 | 2 |
| #23761558 | 2 |
| C79×#2133 | 2 |
| #13606 | 79 |