Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
326 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 64 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. C2×C3×AΓL(1,𝔽9) | C2 | semidirect |
| 2. C3×C4×PSU(3,𝔽2) | C2 | semidirect |
| 4. C3×C4⋊AGL(1,𝔽9) | C2 | semidirect |
| 5. C3×GO+(4,𝔽2)⋊C4 | C2 | semidirect |
| 6. #10596410 | C3 | direct (N × H) |
| 17. C2×AΓL(1,𝔽9) | C2×C3 | semidirect |
| 18. C4×PSU(3,𝔽2) | C2×C3 | semidirect |
| 20. C4⋊AGL(1,𝔽9) | C2×C3 | semidirect |
| 21. GO+(4,𝔽2)⋊C4 | C2×C3 | semidirect |
| 28. C3×PSU(3,𝔽2) | D4 | semidirect |
| 57. C33×C4 | SD16 | semidirect |
| 58. C3×C3⋊Dic3 | SD16 | semidirect |
| 71. PSU(3,𝔽2) | C3×D4 | semidirect |
| 117. C32×C4 | C3×SD16 | semidirect |
| 118. C3⋊Dic3 | C3×SD16 | semidirect |
| 125. C33 | #460 | semidirect |
| 185. C3×C4 | AΓL(1,𝔽9) | semidirect |
| 189. C32 | C3×#460 | semidirect |
| 225. C4 | C3×AΓL(1,𝔽9) | semidirect |
| 228. C3 | #10596410 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×AΓL(1,𝔽9) | 2 |
| C3×C4×PSU(3,𝔽2) | 2 |
| C3×#64231 | 2 |
| C3×C4⋊AGL(1,𝔽9) | 2 |
| C3×GO+(4,𝔽2)⋊C4 | 2 |
| #10596410 | 3 |
| C3×#460 | 9 |