Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
280 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 8. #91227 | C4 | semidirect |
| 13. C3×C5×M32 | C4 | semidirect |
| 14. C3×#3944 | C4 | semidirect |
| 48. C5×M32 | Dic3 | semidirect |
| 49. #3944 | Dic3 | semidirect |
| 72. C3×M32 | AGL(1,𝔽5) | semidirect |
| 144. M32 | ΓL(1,𝔽16) | semidirect |
| 192. C3×C5 | #1377 | semidirect |
| 224. C5 | #67812 | semidirect |
| 234. C3 | #10598671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91221 | 2 |
| D5⋊#812 | 2 |
| C3×D5×M32 | 2 |
| #10598671 | 3 |
| #67812 | 5 |