Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
358 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 3. #10623979 | C2 | semidirect |
| 4. ΓL(1,𝔽16)⋊Dic3 | C2 | semidirect |
| 8. C2×C3⋊Dic15 | C4 | semidirect |
| 9. C2×C5×C3⋊Dic3 | C4 | semidirect |
| 10. D5×C3⋊Dic3 | C4 | semidirect |
| 11. D5×C3⋊Dic3 | C4 | semidirect |
| 66. C2×C3⋊Dic3 | AGL(1,𝔽5) | semidirect |
| 92. C32×C5 | #117 | semidirect |
| 153. C3×C5 | #877 | semidirect |
| 176. C32 | #4130 | semidirect |
| 193. C5 | #63957 | semidirect |
| 204. C3 | #91923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×C3⋊Dic3 | 2 |
| C3×#6763 | 2 |
| #10623979 | 2 |
| ΓL(1,𝔽16)⋊Dic3 | 2 |
| #91923 | 3 |
| #63957 | 5 |