Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
336 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 60. C32×C5 | #125 | semidirect |
| 95. C3×C5 | #870 | semidirect |
| 105. C32 | #4036 | semidirect |
| 114. C5 | #64079 | semidirect |
| 121. C3 | #91388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊(C3⋊Dic15) | 2 |
| C5×C4⋊(C3⋊Dic3) | 2 |
| C32×C4×Dic5 | 2 |
| #10623775 | 2 |
| #10623774 | 2 |
| #91388 | 3 |
| #64079 | 5 |