Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
464 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 3. #11746364 | C2 | semidirect |
| 4. C3×#64763 | C2 | semidirect |
| 5. #11745850 | C2 | semidirect |
| 23. #64763 | D3 | direct (N × H) |
| 151. C5×D3 | #330 | semidirect |
| 189. C3×C5 | C2×#330 | semidirect |
| 216. D3 | #64763 | direct (N × H) |
| 217. C5 | D3×#330 | semidirect |
| 227. C3 | C2×#64763 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D3×#125 | 2 |
| D3×#3935 | 2 |
| #11746364 | 2 |
| C3×#64763 | 2 |
| #11745850 | 2 |
| C2×#64763 | 3 |
| D3×#330 | 5 |