Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
142 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 142 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. #91225 | C3 | direct (N × H) |
| 56. C32×C5 | #108 | semidirect |
| 90. C3×C5 | #819 | semidirect |
| 91. C3×C5 | C3×#108 | semidirect |
| 103. C32 | #3996 | semidirect |
| 114. C5 | C3×#819 | semidirect |
| 119. C3 | C3×#3996 | semidirect |
| 120. C3 | #91225 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6758 | 2 |
| C32×C8×D5 | 2 |
| #91225 | 3 |
| C3×#3996 | 3 |
| C3×#819 | 5 |