Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
150 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C5×C9 | C22 |
| commutator | C2 | C2×C5×C8×C9 |
| Frattini, cosocle | C2×C3×C4 | C22×C3×C5 |
| socle | C22×C3×C5 | C2×C3×C4 |
| prime radical | C23×C3×C5 | C3×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C5×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C5×C8×C9 | C2 | semidirect |
| 9. C9×C22⋊C8 | C5 | direct (N × H) |
| 14. C22×C5×C9 | C8 | semidirect |
| 18. C5×C22⋊C8 | C9 | direct (N × H) |
| 20. C2×C8×C9 | C2×C5 | semidirect |
| 32. C2×C5×C8 | C2×C9 | semidirect |
| 46. C5×C9 | C22⋊C8 | direct (N × H) |
| 54. C22×C9 | C5×C8 | semidirect |
| 58. C22⋊C8 | C5×C9 | direct (N × H) |
| 70. C22×C5 | C8×C9 | semidirect |
| 79. C2×C8 | C2×C5×C9 | semidirect |
| 91. C9 | C5×C22⋊C8 | direct (N × H) |
| 101. C5 | C9×C22⋊C8 | direct (N × H) |
| 104. C22 | C5×C8×C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×C9 | 2 |
| C2×C5×C8×C9 | 2 |
| C3×C5×C22⋊C8 | 3 |
| C9×C22⋊C8 | 5 |