Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
302 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 302 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 |
|---|---|---|
| 6. #91376 | C3 | direct (N × H) |
| 27. C32×Dic5 | Q8 | semidirect |
| 71. C3×Dic5 | Dic6 | semidirect |
| 72. C3×Dic5 | C3×Q8 | semidirect |
| 83. C32×C5 | C4⋊Q8 | semidirect |
| 120. Dic5 | C3×Dic6 | semidirect |
| 128. C3×C5 | #869 | semidirect |
| 129. C3×C5 | C3×C4⋊Q8 | semidirect |
| 145. C32 | #4090 | semidirect |
| 158. C5 | C3×#869 | semidirect |
| 165. C3 | #91376 | direct (N × H) |
| 166. C3 | C3×#4090 | 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 |
| C32×C4×Dic5 | 2 |
| C3×#6668 | 2 |
| C3×#4090 | 3 |
| #91376 | 3 |
| C3×#869 | 5 |