Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
546 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 3. #23761270 | C2 | semidirect |
| 4. #23761269 | C2 | semidirect |
| 5. C79×#1290 | C2 | semidirect |
| 143. #1290 | D79 | semidirect |
| 144. C79 | #7986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #432×D79 | 2 |
| C2×#19098615 | 2 |
| #23761270 | 2 |
| #23761269 | 2 |
| C79×#1290 | 2 |
| #7986 | 79 |