Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
364 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 1. #11752364 | C2 | semidirect |
| 2. #11752361 | C2 | semidirect |
| 4. #11746754 | C2 | semidirect |
| 5. #11746751 | C2 | semidirect |
| 6. #11746742 | C2 | semidirect |
| 7. #11746742 | C2 | semidirect |
| 84. C3×D20 | M16 | semidirect |
| 180. D20 | #208 | semidirect |
| 267. C3×C5 | #1586 | semidirect |
| 314. C5 | #70880 | semidirect |
| 329. C3 | #10604065 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752364 | 2 |
| #11752361 | 2 |
| C3×#65161 | 2 |
| #11746754 | 2 |
| #11746751 | 2 |
| #11746742 | 2 |
| #10604065 | 3 |
| #70880 | 5 |