Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
322 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 322 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 |
|---|---|---|
| 1. C2×C3×Dic30 | C2 | semidirect |
| 3. C32×C4⋊Dic5 | C2 | semidirect |
| 4. C3×#6668 | C2 | semidirect |
| 7. #91365 | C3 | direct (N × H) |
| 17. C2×Dic30 | C2×C3 | semidirect |
| 22. C3×C4⋊Dic5 | D3 | semidirect |
| 23. C3×C4⋊Dic5 | C2×C3 | semidirect |
| 25. #6668 | C2×C3 | semidirect |
| 30. C2×C3×C5×D3 | Q8 | semidirect |
| 66. C4⋊Dic5 | C3×D3 | semidirect |
| 83. C2×C5×D3 | C3×Q8 | semidirect |
| 105. C32×C5 | C22⋊Q8 | semidirect |
| 116. C2×C3×D3 | Dic10 | semidirect |
| 167. C3×C5 | #897 | semidirect |
| 168. C3×C5 | C3×C22⋊Q8 | semidirect |
| 177. C2×D3 | C3×Dic10 | semidirect |
| 192. C32 | #4070 | semidirect |
| 211. C5 | C3×#897 | semidirect |
| 221. C3 | #91365 | direct (N × H) |
| 222. 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×Dic30 | 2 |
| C2×C3×C4×C5×D3 | 2 |
| C32×C4⋊Dic5 | 2 |
| C3×#6668 | 2 |
| C3×(C2×D3)⋊Dic5 | 2 |
| C3×#4070 | 3 |
| #91365 | 3 |
| C3×#897 | 5 |