Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
360 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 72 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. C22×#4002 | C3 | semidirect |
| 7. A4×#170 | C4 | semidirect |
| 29. C22×#170 | C3×C4 | semidirect |
| 37. #4002 | A4 | direct (N × H) |
| 81. C5×A4 | #97 | semidirect |
| 117. #170 | C4×A4 | semidirect |
| 153. C22×C5 | C3×#97 | semidirect |
| 187. A4 | #4002 | direct (N × H) |
| 228. C5 | A4×#97 | semidirect |
| 239. C22 | C3×#4002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×A4×#170 | 2 |
| C4×A4×Dic5 | 2 |
| C22×#4002 | 3 |
| C3×#4002 | 4 |
| A4×#97 | 5 |