Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
156 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C5×C9 | C22⋊C4 |
| commutator | C22 | C2×C4×C5×C9 |
| Frattini, cosocle | C23×C3 | C22×C3×C5 |
| socle | C2×C3×C5 | C3×C22⋊C4 |
| prime radical | C2×C3×C5×D4 | C2×C3 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5×C9 ◁ C23×C5×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×C9×C22⋊C4 | C2 | semidirect |
| 4. C23×C5×C9 | C4 | semidirect |
| 8. C2×C4×C5×C9 | C4 | semidirect |
| 9. C9×#99 | C5 | direct (N × H) |
| 19. C5×#99 | C9 | direct (N × H) |
| 21. C9×C22⋊C4 | C2×C5 | semidirect |
| 33. C5×C22⋊C4 | C2×C9 | semidirect |
| 34. C23×C9 | C4×C5 | semidirect |
| 38. C2×C4×C9 | C4×C5 | semidirect |
| 48. C5×C9 | #99 | direct (N × H) |
| 49. C23×C5 | C4×C9 | semidirect |
| 53. C2×C4×C5 | C4×C9 | semidirect |
| 61. #99 | C5×C9 | direct (N × H) |
| 83. C22⋊C4 | C2×C5×C9 | semidirect |
| 96. C9 | C5×#99 | direct (N × H) |
| 97. C23 | C4×C5×C9 | semidirect |
| 101. C2×C4 | C4×C5×C9 | semidirect |
| 106. C5 | C9×#99 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×C9 | 2 |
| C5×C9×C22⋊C4 | 2 |
| C3×C5×#99 | 3 |
| C9×#99 | 5 |