Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 270 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. C3×#6710 | C2 | semidirect |
| 3. C2×C32×#168 | C2 | semidirect |
| 4. C3×#6650 | C2 | semidirect |
| 5. C3×D3×#168 | C2 | semidirect |
| 7. #91286 | C3 | direct (N × H) |
| 19. #6710 | C2×C3 | semidirect |
| 24. C2×C3×#168 | D3 | semidirect |
| 25. C2×C3×#168 | C2×C3 | semidirect |
| 26. #6650 | C2×C3 | semidirect |
| 27. D3×#168 | C2×C3 | semidirect |
| 67. C2×#168 | C3×D3 | semidirect |
| 100. C32×C5 | #131 | semidirect |
| 156. C3×C5 | #901 | semidirect |
| 157. C3×C5 | C3×#131 | semidirect |
| 174. C32 | #4094 | semidirect |
| 191. C5 | C3×#901 | semidirect |
| 198. C3 | #91286 | direct (N × H) |
| 199. C3 | C3×#4094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#235 | 2 |
| C3×#6710 | 2 |
| C2×C32×#168 | 2 |
| C3×#6650 | 2 |
| C3×D3×#168 | 2 |
| C3×#4094 | 3 |
| #91286 | 3 |
| C3×#901 | 5 |