Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23765173 | C2 | semidirect |
| 5. #23761497 | C2 | semidirect |
| 6. #23761495 | C2 | semidirect |
| 7. C79×#2155 | C2 | semidirect |
| 11. C2×#14579100 | C4 | semidirect |
| 13. C2×C16×D79 | C4 | semidirect |
| 142. #2155 | D79 | semidirect |
| 147. C79 | #12832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098981 | 2 |
| #23765173 | 2 |
| #23763447 | 2 |
| #23763443 | 2 |
| #23761497 | 2 |
| #23761495 | 2 |
| C79×#2155 | 2 |
| #12832 | 79 |