Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
254 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 7. #91388 | C3 | direct (N × H) |
| 92. C32×C5 | #125 | semidirect |
| 142. C3×C5 | #870 | semidirect |
| 143. C3×C5 | C3×#125 | semidirect |
| 163. C32 | #4036 | semidirect |
| 178. C5 | C3×#870 | semidirect |
| 186. C3 | #91388 | direct (N × H) |
| 187. C3 | C3×#4036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4⋊Dic15 | 2 |
| C3×C5×C4⋊Dic3 | 2 |
| C32×C4×Dic5 | 2 |
| C3×Dic3⋊Dic5 | 2 |
| C3×#6669 | 2 |
| C3×#4036 | 3 |
| #91388 | 3 |
| C3×#870 | 5 |