Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 6. C2×#14579072 | C4 | semidirect |
| 7. C2×C4×C79⋊C8 | C4 | semidirect |
| 9. #19098289 | C4 | semidirect |
| 121. C79 | #7214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763166 | 2 |
| #23761734 | 2 |
| C79×#1820 | 2 |
| #7214 | 79 |