Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
336 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 106 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. #11746732 | C2 | semidirect |
| 4. C3×#64861 | C2 | semidirect |
| 5. #11746565 | C2 | semidirect |
| 23. #64861 | D3 | direct (N × H) |
| 164. C5×D3 | #364 | semidirect |
| 208. C3×C5 | C2×#364 | semidirect |
| 242. D3 | #64861 | direct (N × H) |
| 243. C5 | D3×#364 | semidirect |
| 254. C3 | C2×#64861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#3998 | 2 |
| C4×D3×#168 | 2 |
| #11746732 | 2 |
| C3×#64861 | 2 |
| #11746565 | 2 |
| C2×#64861 | 3 |
| D3×#364 | 5 |