Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
206 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 59 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. C4×C5×C3⋊Dic3 | C2 | semidirect |
| 3. C3×#6710 | C2 | semidirect |
| 9. C3×D60 | C4 | semidirect |
| 11. C3×Dic30 | C4 | semidirect |
| 16. #6710 | D3 | semidirect |
| 29. C4×C3⋊Dic3 | D5 | semidirect |
| 35. D60 | Dic3 | semidirect |
| 37. Dic30 | Dic3 | semidirect |
| 85. C32×C5 | #104 | semidirect |
| 137. C3×C5 | #825 | semidirect |
| 138. C3×C5 | #837 | semidirect |
| 158. C32 | #3937 | semidirect |
| 174. C5 | #63568 | semidirect |
| 182. C3 | #90977 | semidirect |
| 183. C3 | #90980 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6817 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C3×#6710 | 2 |
| #90980 | 3 |
| #90977 | 3 |
| #63568 | 5 |