Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
358 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 2. C2×C3×C5×Dic6 | C2 | semidirect |
| 3. C3×C4×Dic15 | C2 | semidirect |
| 4. #10623813 | C2 | semidirect |
| 18. C2×C5×Dic6 | D3 | semidirect |
| 20. C4×Dic15 | D3 | semidirect |
| 31. C2×C3×Dic6 | D5 | semidirect |
| 84. C2×Dic6 | D15 | semidirect |
| 89. C32×C5 | #124 | semidirect |
| 141. C3×C5 | #875 | semidirect |
| 142. C3×C5 | #947 | semidirect |
| 162. C32 | #4093 | semidirect |
| 178. C5 | #63864 | semidirect |
| 186. C3 | #91375 | semidirect |
| 187. C3 | #91836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊D15) | 2 |
| C2×C3×C5×Dic6 | 2 |
| C3×C4×Dic15 | 2 |
| #10623813 | 2 |
| #91836 | 3 |
| #91375 | 3 |
| #63864 | 5 |