Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 1. C32×C42×C5 | C2 | semidirect |
| 3. C3×#6712 | C2 | semidirect |
| 4. #91765 | C3 | direct (N × H) |
| 11. C3×C42×C5 | D3 | semidirect |
| 12. C3×C42×C5 | C2×C3 | semidirect |
| 14. #6712 | C2×C3 | semidirect |
| 22. C32×C42 | D5 | semidirect |
| 36. C42×C5 | C3×D3 | semidirect |
| 55. C3×C42 | C3×D5 | semidirect |
| 56. C3×C42 | D15 | semidirect |
| 59. C32×C5 | #126 | semidirect |
| 88. C42 | C3×D15 | semidirect |
| 90. C3×C5 | #876 | semidirect |
| 91. C3×C5 | C3×#126 | semidirect |
| 104. C32 | #4022 | semidirect |
| 113. C5 | C3×#876 | semidirect |
| 119. C3 | C3×#4022 | semidirect |
| 120. C3 | #91765 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C42×C5 | 2 |
| C3×#6714 | 2 |
| C3×#6712 | 2 |
| #91765 | 3 |
| C3×#4022 | 3 |
| C3×#876 | 5 |