Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
320 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 2. C3×#65368 | C2 | semidirect |
| 5. #11746368 | C2 | semidirect |
| 6. #11745867 | C2 | semidirect |
| 7. #11745861 | C2 | semidirect |
| 26. #65368 | D3 | semidirect |
| 90. C3×#168 | SD16 | semidirect |
| 180. #168 | #215 | semidirect |
| 249. C3×C5 | #1691 | semidirect |
| 289. C5 | #71345 | semidirect |
| 302. C3 | #10601833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5083 | 2 |
| C3×#65368 | 2 |
| #11747008 | 2 |
| #11746882 | 2 |
| #11746368 | 2 |
| #11745867 | 2 |
| #11745861 | 2 |
| #10601833 | 3 |
| #71345 | 5 |