Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
486 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23761734 | C2 | semidirect |
| 3. #23761420 | C2 | semidirect |
| 5. C79×#1740 | C2 | semidirect |
| 6. C2×#14579149 | C4 | semidirect |
| 8. #19098483 | C4 | semidirect |
| 9. #19098480 | C4 | semidirect |
| 16. #19098409 | C4 | semidirect |
| 195. #1740 | D79 | semidirect |
| 199. C79 | #11758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769087 | 2 |
| #23761734 | 2 |
| #23761420 | 2 |
| #23761396 | 2 |
| C79×#1740 | 2 |
| #11758 | 79 |