Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 78 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. C2×C3⋊(C3⋊#170) | C2 | semidirect |
| 3. C3×#6762 | C2 | semidirect |
| 4. #10623976 | C2 | semidirect |
| 5. #10623975 | C2 | semidirect |
| 6. #10623974 | C2 | semidirect |
| 7. D3×C3⋊#170 | C2 | semidirect |
| 25. #6762 | D3 | semidirect |
| 133. C32×C5 | #131 | semidirect |
| 207. C3×C5 | #907 | semidirect |
| 208. C3×C5 | #948 | semidirect |
| 230. C32 | #4131 | semidirect |
| 252. C5 | #63815 | semidirect |
| 261. C3 | #91929 | semidirect |
| 262. C3 | #91990 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6782 | 2 |
| C2×C3⋊(C3⋊#170) | 2 |
| C3×#6762 | 2 |
| #10623976 | 2 |
| #10623975 | 2 |
| #10623974 | 2 |
| D3×C3⋊#170 | 2 |
| #91990 | 3 |
| #91929 | 3 |
| #63815 | 5 |