Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
512 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 160 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. #11746367 | C2 | semidirect |
| 4. C3×#64766 | C2 | semidirect |
| 5. #11745862 | C2 | semidirect |
| 23. #64766 | D3 | direct (N × H) |
| 160. C5×D3 | #333 | semidirect |
| 203. C3×C5 | C2×#333 | semidirect |
| 235. D3 | #64766 | direct (N × H) |
| 236. C5 | D3×#333 | semidirect |
| 247. C3 | C2×#64766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D3×C4⋊Q8 | 2 |
| D3×C4⋊#168 | 2 |
| #11746367 | 2 |
| C3×#64766 | 2 |
| #11745862 | 2 |
| C2×#64766 | 3 |
| D3×#333 | 5 |