Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
568 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 568 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 |
|---|---|---|
| 2. D3×#4002 | C2 | semidirect |
| 3. #11746792 | C2 | semidirect |
| 4. C3×#64921 | C2 | semidirect |
| 5. #11746504 | C2 | semidirect |
| 17. #91231 | C22 | semidirect |
| 18. C3×#4002 | C22 | semidirect |
| 25. #64921 | D3 | direct (N × H) |
| 65. #4002 | C2×D3 | semidirect |
| 204. C5×D3 | #329 | semidirect |
| 263. C3×C5 | C2×#329 | semidirect |
| 309. D3 | #64921 | direct (N × H) |
| 310. C5 | D3×#329 | semidirect |
| 325. C3 | C2×#64921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#4082 | 2 |
| D3×#4002 | 2 |
| #11746792 | 2 |
| C3×#64921 | 2 |
| #11746504 | 2 |
| C2×#64921 | 3 |
| D3×#329 | 5 |