Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
460 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23764377 | C2 | semidirect |
| 4. #23762159 | C2 | semidirect |
| 5. #23761856 | C2 | semidirect |
| 7. C79×#1744 | C2 | semidirect |
| 10. #19098961 | C4 | semidirect |
| 11. #19098936 | C4 | semidirect |
| 12. #19098914 | C4 | semidirect |
| 13. #19098910 | C4 | semidirect |
| 168. #1744 | D79 | semidirect |
| 172. C79 | #9854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773959 | 2 |
| #23764377 | 2 |
| #23764228 | 2 |
| #23762159 | 2 |
| #23761856 | 2 |
| #23761852 | 2 |
| C79×#1744 | 2 |
| #9854 | 79 |