Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
708 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 135 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. A4×#681 | C2 | semidirect |
| 3. C2×A4×#168 | C2 | semidirect |
| 4. C22×#4094 | C3 | semidirect |
| 17. C22×#681 | C2×C3 | semidirect |
| 18. C23×#168 | C2×C3 | semidirect |
| 41. #4094 | A4 | direct (N × H) |
| 87. #681 | C2×A4 | semidirect |
| 96. C2×#168 | C2×A4 | semidirect |
| 105. C5×A4 | #131 | semidirect |
| 178. C22×C5 | C3×#131 | semidirect |
| 218. A4 | #4094 | direct (N × H) |
| 253. C5 | A4×#131 | semidirect |
| 261. C22 | C3×#4094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×A4×#41 | 2 |
| A4×#681 | 2 |
| C2×A4×#168 | 2 |
| C22×#4094 | 3 |
| C3×#4094 | 4 |
| A4×#131 | 5 |