Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
530 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23764228 | C2 | semidirect |
| 3. C4×#14579072 | C2 | semidirect |
| 4. #23762155 | C2 | semidirect |
| 5. #23761851 | C2 | semidirect |
| 6. #23761850 | C2 | semidirect |
| 7. C79×#1962 | C2 | semidirect |
| 9. #19098966 | C4 | semidirect |
| 10. #19098939 | C4 | semidirect |
| 11. #19098911 | C4 | semidirect |
| 12. #19098909 | C4 | semidirect |
| 149. C79⋊C8 | #104 | semidirect |
| 179. #1962 | D79 | semidirect |
| 184. C79 | #9849 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773975 | 2 |
| #23764228 | 2 |
| C4×#14579072 | 2 |
| #23762155 | 2 |
| #23761851 | 2 |
| #23761850 | 2 |
| C79×#1962 | 2 |
| #9849 | 79 |