Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
320 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 4. #11746941 | C2 | semidirect |
| 5. #11745867 | C2 | semidirect |
| 6. #11745862 | C2 | semidirect |
| 7. #11745859 | C2 | semidirect |
| 90. C3×#168 | SD16 | semidirect |
| 180. #168 | #214 | semidirect |
| 249. C3×C5 | #1691 | semidirect |
| 289. C5 | #70872 | semidirect |
| 302. C3 | #10601929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751120 | 2 |
| C5×#5008 | 2 |
| C3×#65301 | 2 |
| #11746941 | 2 |
| #11745867 | 2 |
| #11745862 | 2 |
| #11745859 | 2 |
| #10601929 | 3 |
| #70872 | 5 |