Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
346 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 346 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. C22×C3×C5×Dic3 | C2 | semidirect |
| 3. #10623913 | C2 | semidirect |
| 4. #10623815 | C2 | semidirect |
| 5. #10623811 | C2 | semidirect |
| 18. C22×C5×Dic3 | D3 | semidirect |
| 37. C22×C3×Dic3 | D5 | semidirect |
| 98. C22×Dic3 | D15 | semidirect |
| 106. C32×C5 | #123 | semidirect |
| 168. C3×C5 | #929 | semidirect |
| 169. C3×C5 | #935 | semidirect |
| 194. C32 | #4075 | semidirect |
| 213. C5 | #63961 | semidirect |
| 223. C3 | #91536 | semidirect |
| 224. C3 | #91818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1220 | 2 |
| C22×C3×C5×Dic3 | 2 |
| #10623913 | 2 |
| #10623815 | 2 |
| #10623811 | 2 |
| #91818 | 3 |
| #91536 | 3 |
| #63961 | 5 |