Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
272 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 80 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×#65167 | C2 | semidirect |
| 3. #11746311 | C2 | semidirect |
| 5. #11745941 | C2 | semidirect |
| 6. #11745927 | C2 | semidirect |
| 22. #65167 | D3 | semidirect |
| 201. C3×C5 | #2228 | semidirect |
| 234. C5 | #71356 | semidirect |
| 246. C3 | #10599973 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65167 | 2 |
| Dic5×D24 | 2 |
| #11746311 | 2 |
| C5×#4491 | 2 |
| #11745941 | 2 |
| #11745927 | 2 |
| #11745893 | 2 |
| #10599973 | 3 |
| #71356 | 5 |