Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
322 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 322 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. #23761574 | C2 | semidirect |
| 5. C2×#14579153 | C4 | semidirect |
| 8. #19098917 | C4 | semidirect |
| 13. C4×#11929608 | C4 | semidirect |
| 136. C79 | #13604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773800 | 2 |
| #23765085 | 2 |
| #23761574 | 2 |
| C79×#2126 | 2 |
| #13604 | 79 |