Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
320 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 86 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. C3×#65139 | C2 | semidirect |
| 4. #11746846 | C2 | semidirect |
| 5. #11746301 | C2 | semidirect |
| 7. #11745861 | C2 | semidirect |
| 27. #65139 | D3 | semidirect |
| 248. C3×C5 | #1678 | semidirect |
| 289. C5 | #71150 | semidirect |
| 302. C3 | #10599203 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65139 | 2 |
| #11747060 | 2 |
| #11746901 | 2 |
| #11746846 | 2 |
| #11746301 | 2 |
| C5×#4485 | 2 |
| #11745861 | 2 |
| #10599203 | 3 |
| #71150 | 5 |