Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
190 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 58 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. #91234 | C3 | direct (N × H) |
| 65. C32×C5 | #101 | semidirect |
| 105. C3×C5 | #836 | semidirect |
| 106. C3×C5 | C3×#101 | semidirect |
| 121. C32 | #4005 | semidirect |
| 133. C5 | C3×#836 | semidirect |
| 139. C3 | C3×#4005 | semidirect |
| 140. C3 | #91234 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Dic10 | 2 |
| C3×#6762 | 2 |
| #91234 | 3 |
| C3×#4005 | 3 |
| C3×#836 | 5 |