Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 116 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×C5×Dic3⋊C4 | C2 | semidirect |
| 5. C5×#876 | C3 | direct (N × H) |
| 9. C3×#876 | C5 | direct (N × H) |
| 13. C3×C42×C5 | D3 | semidirect |
| 14. C3×C42×C5 | C2×C3 | semidirect |
| 16. C5×Dic3⋊C4 | C2×C3 | semidirect |
| 22. C32×C42 | C2×C5 | semidirect |
| 24. C3×Dic3⋊C4 | C2×C5 | semidirect |
| 33. #876 | C3×C5 | direct (N × H) |
| 38. C42×C5 | C3×D3 | semidirect |
| 55. C3×C42 | C5×D3 | semidirect |
| 56. C3×C42 | C2×C3×C5 | semidirect |
| 58. Dic3⋊C4 | C2×C3×C5 | semidirect |
| 59. C32×C5 | #126 | semidirect |
| 88. C42 | C3×C5×D3 | semidirect |
| 90. C3×C5 | #876 | direct (N × H) |
| 91. C3×C5 | C3×#126 | semidirect |
| 104. C32 | C5×#126 | semidirect |
| 113. C5 | C3×#876 | direct (N × H) |
| 119. C3 | C5×#876 | direct (N × H) |
| 120. C3 | C3×C5×#126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C42×C5 | 2 |
| C3×C5×(C2×D3)⋊C4 | 2 |
| C3×C5×Dic3⋊C4 | 2 |
| C3×C5×#126 | 3 |
| C5×#876 | 3 |
| C3×#876 | 5 |