Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
334 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 112 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×C32×Dic10 | C2 | semidirect |
| 3. C3×C4⋊Dic15 | C2 | semidirect |
| 4. C3×#6669 | C2 | semidirect |
| 7. #91369 | C3 | direct (N × H) |
| 19. C2×C3×Dic10 | D3 | semidirect |
| 20. C2×C3×Dic10 | C2×C3 | semidirect |
| 21. C4⋊Dic15 | C2×C3 | semidirect |
| 25. #6669 | C2×C3 | semidirect |
| 30. C2×C3×C5×D3 | Q8 | semidirect |
| 65. C2×Dic10 | C3×D3 | semidirect |
| 84. C2×C5×D3 | C3×Q8 | semidirect |
| 106. C32×C5 | C22⋊Q8 | semidirect |
| 117. C2×C3×D3 | Dic10 | semidirect |
| 169. C3×C5 | #946 | semidirect |
| 170. C3×C5 | C3×C22⋊Q8 | semidirect |
| 179. C2×D3 | C3×Dic10 | semidirect |
| 194. C32 | #4070 | semidirect |
| 213. C5 | C3×#946 | semidirect |
| 223. C3 | #91369 | direct (N × H) |
| 224. C3 | C3×#4070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×C5×D3 | 2 |
| C2×C32×Dic10 | 2 |
| C3×C4⋊Dic15 | 2 |
| C3×#6669 | 2 |
| C3×(C2×D3)⋊Dic5 | 2 |
| C3×#4070 | 3 |
| #91369 | 3 |
| C3×#946 | 5 |