Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
498 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 111 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. #23764319 | C2 | semidirect |
| 3. C4×#14579092 | C2 | semidirect |
| 4. #23761895 | C2 | semidirect |
| 5. #23761894 | C2 | semidirect |
| 6. #23761687 | C2 | semidirect |
| 7. C79×#1980 | C2 | semidirect |
| 9. #19098966 | C4 | semidirect |
| 10. #19098939 | C4 | semidirect |
| 11. #19098911 | C4 | semidirect |
| 12. #19098909 | C4 | semidirect |
| 171. C79⋊C8 | #104 | semidirect |
| 204. #1980 | D79 | semidirect |
| 209. C79 | #9721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773975 | 2 |
| #23764319 | 2 |
| C4×#14579092 | 2 |
| #23761895 | 2 |
| #23761894 | 2 |
| #23761687 | 2 |
| C79×#1980 | 2 |
| #9721 | 79 |