Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
350 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 91 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×Dic30 | C2 | semidirect |
| 3. C3×C4⋊Dic15 | C2 | semidirect |
| 4. #10623831 | C2 | semidirect |
| 16. C2×Dic30 | D3 | semidirect |
| 21. C4⋊Dic15 | D3 | semidirect |
| 30. C2×C5×C3⋊D3 | Q8 | semidirect |
| 110. C32×C5 | C22⋊Q8 | semidirect |
| 121. C2×C3⋊D3 | Dic10 | semidirect |
| 175. C3×C5 | #897 | semidirect |
| 176. C3×C5 | #946 | semidirect |
| 203. C32 | #4070 | semidirect |
| 223. C5 | #63871 | semidirect |
| 233. C3 | #91365 | semidirect |
| 234. C3 | #91369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×C3⋊D3 | 2 |
| C2×C3×Dic30 | 2 |
| C3×C4⋊Dic15 | 2 |
| #10623831 | 2 |
| #10623830 | 2 |
| #91369 | 3 |
| #91365 | 3 |
| #63871 | 5 |