Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
456 conjugacy classes of subgroups.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C5×C3⋊(C3⋊C8) | C2 | direct (N × H) |
| 7. C5×C3⋊(C3⋊C8) | C22 | direct (N × H) |
| 8. C22×C3⋊(C3⋊C8) | C5 | direct (N × H) |
| 11. C22×C32×C5 | C8 | semidirect |
| 17. C2×C3⋊(C3⋊C8) | C2×C5 | direct (N × H) |
| 23. C2×C32×C5 | C2×C8 | semidirect |
| 30. C3⋊(C3⋊C8) | C22×C5 | direct (N × H) |
| 31. C22×C3×C5 | C3⋊C8 | semidirect |
| 37. C32×C5 | C22×C8 | semidirect |
| 42. C22×C32 | C5×C8 | semidirect |
| 47. C2×C3×C5 | C2×C3⋊C8 | semidirect |
| 53. C22×C5 | C3⋊(C3⋊C8) | direct (N × H) |
| 57. C2×C32 | C2×C5×C8 | semidirect |
| 61. C3×C5 | C22×C3⋊C8 | semidirect |
| 62. C22×C3 | C5×C3⋊C8 | semidirect |
| 66. C2×C5 | C2×C3⋊(C3⋊C8) | direct (N × H) |
| 68. C32 | C22×C5×C8 | semidirect |
| 73. C2×C3 | C2×C5×C3⋊C8 | semidirect |
| 75. C5 | C22×C3⋊(C3⋊C8) | direct (N × H) |
| 76. C22 | C5×C3⋊(C3⋊C8) | direct (N × H) |
| 80. C3 | C22×C5×C3⋊C8 | semidirect |
| 81. C2 | C2×C5×C3⋊(C3⋊C8) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C4×C5 | 2 |
| C2×C5×C3⋊(C3⋊C8) | 2 |
| C22×C5×C3⋊C8 | 3 |
| C22×C3⋊(C3⋊C8) | 5 |