Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
214 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 48 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 |
| 68. C5×A4 | M32 | semidirect |
| 121. C22×C5 | #812 | semidirect |
| 147. A4 | #3998 | semidirect |
| 175. C5 | #73104 | semidirect |
| 183. C22 | #91227 | 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 |
| #10604872 | 3 |
| #91227 | 4 |
| #73104 | 5 |