Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×C3⋊#674 | C4 | semidirect |
| 13. C3×C5×M32 | C4 | semidirect |
| 14. C3×#3944 | C4 | semidirect |
| 48. C5×M32 | Dic3 | semidirect |
| 49. #3944 | Dic3 | semidirect |
| 71. C3×M32 | AGL(1,𝔽5) | semidirect |
| 142. M32 | ΓL(1,𝔽16) | semidirect |
| 189. C3×C5 | #1378 | semidirect |
| 220. C5 | #67814 | semidirect |
| 230. C3 | #10598672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752377 | 2 |
| C2×#91219 | 2 |
| C3×D5×M32 | 2 |
| #10598672 | 3 |
| #67814 | 5 |