Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
320 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 57 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. #23765086 | C2 | semidirect |
| 3. #23765073 | C2 | semidirect |
| 4. #23761576 | C2 | semidirect |
| 5. #23761574 | C2 | semidirect |
| 6. #23761557 | C2 | semidirect |
| 7. C79×#1406 | C2 | semidirect |
| 8. #19099167 | C4 | semidirect |
| 10. #19098935 | C4 | semidirect |
| 11. #19098932 | C4 | semidirect |
| 17. #19098625 | C4 | semidirect |
| 166. #1406 | D79 | semidirect |
| 167. C79 | #13606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774456 | 2 |
| #23765086 | 2 |
| #23765073 | 2 |
| #23761576 | 2 |
| #23761574 | 2 |
| #23761557 | 2 |
| C79×#1406 | 2 |
| #13606 | 79 |