Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
116 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 40 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. C5×A4⋊C8 | C3 | direct (N × H) |
| 6. C3×A4⋊C8 | C5 | direct (N × H) |
| 12. C3×C5×A4 | C8 | semidirect |
| 24. A4⋊C8 | C3×C5 | direct (N × H) |
| 34. C22×C3×C5 | C3⋊C8 | semidirect |
| 36. C5×A4 | C3×C8 | semidirect |
| 52. C3×A4 | C5×C8 | semidirect |
| 70. C22×C5 | C3×C3⋊C8 | semidirect |
| 79. C3×C5 | A4⋊C8 | direct (N × H) |
| 82. C22×C3 | C5×C3⋊C8 | semidirect |
| 84. A4 | C3×C5×C8 | semidirect |
| 103. C5 | C3×A4⋊C8 | direct (N × H) |
| 106. C22 | C3×C5×C3⋊C8 | semidirect |
| 111. C3 | C5×A4⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×A4 | 2 |
| C5×A4⋊C8 | 3 |
| C3×C5×C22⋊C8 | 3 |
| C3×C5×C3⋊C8 | 4 |
| C3×A4⋊C8 | 5 |