Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
306 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 128 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. #91340 | C3 | direct (N × H) |
| 10. C3×Dic30 | C4 | semidirect |
| 30. C3×C5×Dic3 | Q8 | semidirect |
| 44. Dic30 | C3×C4 | semidirect |
| 82. C5×Dic3 | C3×Q8 | semidirect |
| 94. C32×C5 | C4×Q8 | semidirect |
| 106. C3×Dic3 | Dic10 | semidirect |
| 146. C3×C5 | #887 | semidirect |
| 147. C3×C5 | C3×C4×Q8 | semidirect |
| 162. Dic3 | C3×Dic10 | semidirect |
| 166. C32 | C4×Dic10 | semidirect |
| 182. C5 | C3×#887 | semidirect |
| 190. C3 | #91340 | direct (N × H) |
| 191. C3 | C3×C4×Dic10 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic30 | 2 |
| C3×C4×C5×Dic3 | 2 |
| C32×C4⋊Dic5 | 2 |
| C3×#6669 | 2 |
| C3×Dic3×Dic5 | 2 |
| C3×C4×Dic10 | 3 |
| #91340 | 3 |
| C3×#887 | 5 |