Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
274 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 74 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. C3×#6712 | C2 | semidirect |
| 3. C3×C5×C4⋊Dic3 | C2 | semidirect |
| 4. Dic3⋊Dic15 | C2 | semidirect |
| 7. Dic3×Dic15 | C2 | semidirect |
| 25. #6712 | D3 | semidirect |
| 27. C5×C4⋊Dic3 | D3 | semidirect |
| 45. C3×C4⋊Dic3 | D5 | semidirect |
| 124. C4⋊Dic3 | D15 | semidirect |
| 129. C32×C5 | #126 | semidirect |
| 199. C3×C5 | #898 | semidirect |
| 200. C3×C5 | #898 | semidirect |
| 231. C32 | #4044 | semidirect |
| 251. C5 | #63848 | semidirect |
| 263. C3 | #91337 | semidirect |
| 264. C3 | #91787 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623908 | 2 |
| C3×#6712 | 2 |
| C3×C5×C4⋊Dic3 | 2 |
| Dic3⋊Dic15 | 2 |
| #10623813 | 2 |
| Dic3×Dic15 | 2 |
| #91787 | 3 |
| #91337 | 3 |
| #63848 | 5 |