Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
220 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 54 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×#674 | C2 | semidirect |
| 3. C22×#3998 | C3 | semidirect |
| 13. C22×#674 | C2×C3 | semidirect |
| 31. #3998 | A4 | direct (N × H) |
| 61. #674 | C2×A4 | semidirect |
| 68. C5×A4 | M32 | semidirect |
| 121. C22×C5 | C3×M32 | semidirect |
| 147. A4 | #3998 | direct (N × H) |
| 175. C5 | A4×M32 | semidirect |
| 183. C22 | C3×#3998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×A4×#168 | 2 |
| A4×#674 | 2 |
| C22×#3998 | 3 |
| C3×#3998 | 4 |
| A4×M32 | 5 |