Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
116 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | A4×D15 |
| commutator, hypocenter | C22×C3×C5 | C3×C8 |
| Fitting, cosocle | C22×C3×C4×C5 | C2×C3 |
| socle | C23×C3×C5 | C3×C4 |
| prime radical | C2×C3×C5×A4 | C4 |
| LCS | G ▷ C22×C3×C5 | |
| UCS | C1 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C3⋊#168 | C3 | semidirect |
| 12. C3×C5×A4 | C8 | semidirect |
| 22. C3⋊#168 | A4 | direct (N × H) |
| 34. C22×C3×C5 | C3×C8 | semidirect |
| 36. C5×A4 | C3⋊C8 | semidirect |
| 52. C3×A4 | #168 | semidirect |
| 70. C22×C5 | C3×C3⋊C8 | semidirect |
| 79. C3×C5 | C8×A4 | semidirect |
| 82. C22×C3 | C3×#168 | semidirect |
| 84. A4 | C3⋊#168 | direct (N × H) |
| 103. C5 | A4×C3⋊C8 | semidirect |
| 106. C22 | C3×C3⋊#168 | semidirect |
| 111. C3 | A4×#168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×A4 | 2 |
| C22×C3⋊#168 | 3 |
| A4×#168 | 3 |
| C3×C3⋊#168 | 4 |
| A4×C3⋊C8 | 5 |