Finite Group DatabasebetaFinite Group DatabasebetaOrder 2160.
108 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 26 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 |
|---|---|---|
| 1. C3×C5⋊PSU(3,𝔽2) | C2 | semidirect |
| 3. C3×C5×AGL(1,𝔽9) | C2 | semidirect |
| 4. AGL(1,𝔽9)⋊D5 | C3 | direct (N × H) |
| 9. C5⋊PSU(3,𝔽2) | C2×C3 | semidirect |
| 11. C5×AGL(1,𝔽9) | C2×C3 | semidirect |
| 17. C3×AGL(1,𝔽9) | D5 | semidirect |
| 23. C33×C5 | SD16 | semidirect |
| 39. AGL(1,𝔽9) | C3×D5 | semidirect |
| 49. C32×C5 | C3×SD16 | semidirect |
| 63. C33 | #677 | semidirect |
| 79. C3×C5 | AΓL(1,𝔽9) | semidirect |
| 88. C32 | C3×#677 | semidirect |
| 98. C5 | C3×AΓL(1,𝔽9) | semidirect |
| 104. C3 | AGL(1,𝔽9)⋊D5 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5⋊PSU(3,𝔽2) | 2 |
| C3×#157⋊D5 | 2 |
| C3×C5×AGL(1,𝔽9) | 2 |
| AGL(1,𝔽9)⋊D5 | 3 |
| C3×AΓL(1,𝔽9) | 5 |
| C3×#677 | 9 |