Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
302 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 25. C3⋊Dic15 | Q8 | semidirect |
| 83. C32×C5 | C4⋊Q8 | semidirect |
| 128. C3×C5 | #944 | semidirect |
| 129. C3×C5 | #944 | semidirect |
| 145. C32 | #4090 | semidirect |
| 158. C5 | #63873 | semidirect |
| 165. C3 | #91385 | semidirect |
| 166. C3 | #91833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic30 | 2 |
| C2×C3×C5×Dic6 | 2 |
| C4×C3⋊Dic15 | 2 |
| #10623815 | 2 |
| #91833 | 3 |
| #91385 | 3 |
| #63873 | 5 |