Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
514 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23763571 | C2 | semidirect |
| 3. #23761852 | C2 | semidirect |
| 4. #23761851 | C2 | semidirect |
| 5. #23761850 | C2 | semidirect |
| 6. C2×#19098285 | C2 | semidirect |
| 7. C79×#1492 | C2 | semidirect |
| 180. #1492 | D79 | semidirect |
| 182. C79 | #9862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773826 | 2 |
| #23763571 | 2 |
| #23761852 | 2 |
| #23761851 | 2 |
| #23761850 | 2 |
| C2×#19098285 | 2 |
| C79×#1492 | 2 |
| #9862 | 79 |