Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
324 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 8. C2×C3×#681 | C4 | semidirect |
| 9. C22×C3×#168 | C4 | semidirect |
| 10. #91120 | C4 | semidirect |
| 45. C2×#681 | Dic3 | semidirect |
| 46. C22×#168 | Dic3 | semidirect |
| 230. C3×C5 | #1395 | semidirect |
| 275. C5 | #67692 | semidirect |
| 289. C3 | #10598188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751338 | 2 |
| C5×#5240 | 2 |
| C3×#65523 | 2 |
| #10598188 | 3 |
| #67692 | 5 |