Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
262 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 45 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. C3×#6763 | C2 | semidirect |
| 4. C22×C3⋊D15 | C4 | semidirect |
| 7. C2×C5×C3⋊Dic3 | C4 | semidirect |
| 12. #6763 | D3 | semidirect |
| 45. C2×C3⋊Dic3 | AGL(1,𝔽5) | semidirect |
| 66. C32×C5 | #99 | semidirect |
| 114. C3×C5 | #806 | semidirect |
| 134. C32 | #3999 | semidirect |
| 149. C5 | #63581 | semidirect |
| 158. C3 | #91173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67139 | 2 |
| C3×#6763 | 2 |
| #91173 | 3 |
| #63581 | 5 |