Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
268 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 268 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. C2×C3×C3⋊#168 | C2 | semidirect |
| 3. C32×#681 | C2 | semidirect |
| 4. C3×#6650 | C2 | semidirect |
| 5. C3×D3×#168 | C2 | semidirect |
| 7. #91288 | C3 | direct (N × H) |
| 19. C2×C3⋊#168 | C2×C3 | semidirect |
| 22. C3×#681 | D3 | semidirect |
| 23. C3×#681 | C2×C3 | semidirect |
| 26. #6650 | C2×C3 | semidirect |
| 27. D3×#168 | C2×C3 | semidirect |
| 64. #681 | C3×D3 | semidirect |
| 99. C32×C5 | #131 | semidirect |
| 154. C3×C5 | #907 | semidirect |
| 155. C3×C5 | C3×#131 | semidirect |
| 172. C32 | #4094 | semidirect |
| 189. C5 | C3×#907 | semidirect |
| 196. C3 | #91288 | direct (N × H) |
| 197. 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 |
| C2×C3×C3⋊#168 | 2 |
| C32×#681 | 2 |
| C3×#6650 | 2 |
| C3×D3×#168 | 2 |
| C3×#4094 | 3 |
| #91288 | 3 |
| C3×#907 | 5 |