Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
490 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23761911 | C2 | semidirect |
| 4. #23761293 | C2 | semidirect |
| 7. #19098922 | C4 | semidirect |
| 23. #14579161 | C2×C4 | semidirect |
| 33. #14579072 | C2×C4 | semidirect |
| 147. C79 | #9439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773786 | 2 |
| #23762024 | 2 |
| #23761911 | 2 |
| #23761293 | 2 |
| C79×#2372 | 2 |
| #9439 | 79 |