Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
196 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 64 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×C4×C5×Dic3 | C2 | semidirect |
| 3. C32×#681 | C2 | semidirect |
| 5. #90980 | C3 | direct (N × H) |
| 8. C3×D60 | C4 | semidirect |
| 10. C3×Dic30 | C4 | semidirect |
| 17. C4×C5×Dic3 | C2×C3 | semidirect |
| 19. C3×#681 | D3 | semidirect |
| 20. C3×#681 | C2×C3 | semidirect |
| 30. C3×C4×Dic3 | D5 | semidirect |
| 36. D60 | C3×C4 | semidirect |
| 38. Dic30 | C3×C4 | semidirect |
| 54. #681 | C3×D3 | semidirect |
| 83. C4×Dic3 | C3×D5 | semidirect |
| 84. C32×C5 | #104 | semidirect |
| 136. C3×C5 | #825 | semidirect |
| 137. C3×C5 | C3×#104 | semidirect |
| 156. C32 | #3937 | semidirect |
| 172. C5 | C3×#825 | semidirect |
| 180. C3 | #90980 | direct (N × H) |
| 181. C3 | C3×#3937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6817 | 2 |
| C3×C4×C5×Dic3 | 2 |
| C32×#681 | 2 |
| C3×#3937 | 3 |
| #90980 | 3 |
| C3×#825 | 5 |