Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
310 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 310 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. #91389 | C3 | direct (N × H) |
| 26. C3×C5×Dic3 | Q8 | semidirect |
| 74. C5×Dic3 | C3×Q8 | semidirect |
| 84. C32×C5 | C4⋊Q8 | semidirect |
| 95. C3×Dic3 | Dic10 | semidirect |
| 130. C3×C5 | #944 | semidirect |
| 131. C3×C5 | C3×C4⋊Q8 | semidirect |
| 144. Dic3 | C3×Dic10 | semidirect |
| 147. C32 | #4015 | semidirect |
| 160. C5 | C3×#944 | semidirect |
| 167. C3 | #91389 | direct (N × H) |
| 168. C3 | C3×#4015 | 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×C32×Dic10 | 2 |
| C3×C4×C5×Dic3 | 2 |
| C3×Dic3⋊Dic5 | 2 |
| C3×#4015 | 3 |
| #91389 | 3 |
| C3×#944 | 5 |