Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 260 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×C5×#108 | C3 | semidirect |
| 8. A4×#108 | C5 | direct (N × H) |
| 33. C5×#108 | A4 | direct (N × H) |
| 34. C22×#108 | C3×C5 | semidirect |
| 69. C5×A4 | #108 | direct (N × H) |
| 107. #108 | C5×A4 | direct (N × H) |
| 122. C22×C5 | C3×#108 | semidirect |
| 149. A4 | C5×#108 | direct (N × H) |
| 177. C5 | A4×#108 | direct (N × H) |
| 185. C22 | C3×C5×#108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×A4×M16 | 2 |
| C2×C5×C8×A4 | 2 |
| C22×C5×#108 | 3 |
| C3×C5×#108 | 4 |
| A4×#108 | 5 |