Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
388 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 71 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. #23761570 | C2 | semidirect |
| 5. #19099120 | C4 | semidirect |
| 6. #19098927 | C4 | semidirect |
| 13. C4×#11929608 | C4 | semidirect |
| 22. #14579153 | C2×C4 | semidirect |
| 33. #14579072 | C2×C4 | semidirect |
| 155. C79 | #13595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773774 | 2 |
| C2×#19098356 | 2 |
| #23761570 | 2 |
| C2×#353×C79 | 2 |
| #13595 | 79 |