Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
268 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 106 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×C3×C3⋊#168 | C2 | semidirect |
| 4. #10623796 | C2 | semidirect |
| 5. D3×C3⋊#168 | C2 | semidirect |
| 24. C2×C3⋊#168 | D3 | semidirect |
| 99. C32×C5 | #131 | semidirect |
| 154. C3×C5 | #901 | semidirect |
| 155. C3×C5 | #948 | semidirect |
| 172. C32 | #4094 | semidirect |
| 189. C5 | #63814 | semidirect |
| 196. C3 | #91286 | semidirect |
| 197. C3 | #91837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#235 | 2 |
| #10623904 | 2 |
| C2×C3×C3⋊#168 | 2 |
| #10623796 | 2 |
| D3×C3⋊#168 | 2 |
| #91837 | 3 |
| #91286 | 3 |
| #63814 | 5 |