Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
372 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 120 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. #10623904 | C2 | semidirect |
| 3. C2×C32×#168 | C2 | semidirect |
| 4. #10623755 | C2 | semidirect |
| 5. C3⋊D3×#168 | C2 | semidirect |
| 18. C2×C3×#168 | D3 | semidirect |
| 48. C2×#168 | C3⋊D3 | semidirect |
| 67. C32×C5 | #131 | semidirect |
| 106. C3×C5 | #901 | semidirect |
| 115. C32 | #4094 | semidirect |
| 127. C5 | #64110 | semidirect |
| 133. C3 | #91286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3828 | 2 |
| #10623904 | 2 |
| C2×C32×#168 | 2 |
| #10623755 | 2 |
| C3⋊D3×#168 | 2 |
| #91286 | 3 |
| #64110 | 5 |