Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
134 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 82 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×C3⋊#674 | C2 | direct (N × H) |
| 3. C2×C3⋊#674 | C3 | direct (N × H) |
| 12. C3⋊#674 | C2×C3 | direct (N × H) |
| 31. C2×C32×C5 | C16 | semidirect |
| 52. C32×C5 | C2×C16 | semidirect |
| 62. C2×C3×C5 | C3⋊C16 | semidirect |
| 63. C2×C3×C5 | C3×C16 | semidirect |
| 78. C2×C32 | #674 | semidirect |
| 83. C3×C5 | C2×C3⋊C16 | semidirect |
| 84. C3×C5 | C2×C3×C16 | semidirect |
| 94. C2×C5 | C3×C3⋊C16 | semidirect |
| 96. C32 | C2×#674 | semidirect |
| 102. C2×C3 | C3×#674 | semidirect |
| 103. C2×C3 | C3⋊#674 | direct (N × H) |
| 106. C5 | C2×C3×C3⋊C16 | semidirect |
| 111. C3 | C2×C3×#674 | semidirect |
| 112. C3 | C2×C3⋊#674 | direct (N × H) |
| 113. C2 | C3×C3⋊#674 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#168 | 2 |
| C3×C3⋊#674 | 2 |
| C2×C3⋊#674 | 3 |
| C2×C3×#674 | 3 |
| C2×C3×C3⋊C16 | 5 |