Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
356 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 100 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. #11750782 | C2 | semidirect |
| 3. #11746930 | C2 | semidirect |
| 4. #11746929 | C2 | semidirect |
| 7. C3×C8×#168 | C2 | semidirect |
| 29. C8×#168 | D3 | semidirect |
| 220. C3×C5 | #1711 | semidirect |
| 255. C5 | #68061 | semidirect |
| 266. C3 | #10601976 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750782 | 2 |
| C5×#4694 | 2 |
| #11746930 | 2 |
| #11746929 | 2 |
| #11746906 | 2 |
| C3×C8×#168 | 2 |
| #10601976 | 3 |
| #68061 | 5 |