Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
420 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23762037 | C2 | semidirect |
| 4. #23761952 | C2 | semidirect |
| 6. #23761265 | C2 | semidirect |
| 7. C79×#1291 | C2 | semidirect |
| 10. #19098968 | C4 | semidirect |
| 11. #19098936 | C4 | semidirect |
| 12. #19098914 | C4 | semidirect |
| 13. #19098910 | C4 | semidirect |
| 165. #1291 | D79 | semidirect |
| 167. C79 | #9415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774118 | 2 |
| #23772470 | 2 |
| #23762037 | 2 |
| #23761952 | 2 |
| #23761948 | 2 |
| #23761265 | 2 |
| C79×#1291 | 2 |
| #9415 | 79 |