Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
260 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 260 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 |
|---|---|---|
| 3. C22×#3996 | C3 | semidirect |
| 36. #3996 | A4 | direct (N × H) |
| 77. C5×A4 | #108 | semidirect |
| 130. C22×C5 | C3×#108 | semidirect |
| 165. A4 | #3996 | direct (N × H) |
| 195. C5 | A4×#108 | semidirect |
| 204. C22 | C3×#3996 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#700 | 2 |
| C8×D5×A4 | 2 |
| C22×#3996 | 3 |
| C3×#3996 | 4 |
| A4×#108 | 5 |