Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
440 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 150 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×C4×3−1+2 | C2 | semidirect |
| 2. C3×#611⋊C3 | C2 | semidirect |
| 3. C3×C4⋊AGL(1,ℤ/9) | C2 | semidirect |
| 4. C3×C4×AGL(1,ℤ/9) | C2 | semidirect |
| 5. C3×3−1+2⋊Q8 | C2 | semidirect |
| 7. #3697⋊C3 | C3 | direct (N × H) |
| 8. C3×#3697 | C3 | semidirect |
| 20. C2×C4×3−1+2 | C2×C3 | semidirect |
| 22. C2×C3×C4×C9 | C2×C3 | semidirect |
| 23. #611⋊C3 | C2×C3 | semidirect |
| 24. C3×#611 | C2×C3 | semidirect |
| 25. C4⋊AGL(1,ℤ/9) | C2×C3 | semidirect |
| 26. C4×AGL(1,ℤ/9) | C2×C3 | semidirect |
| 27. 3−1+2⋊Q8 | C2×C3 | semidirect |
| 28. C3×D36 | C2×C3 | semidirect |
| 29. C3×C4×D9 | C2×C3 | semidirect |
| 30. C3×Dic18 | C2×C3 | semidirect |
| 37. #3697 | C32 | semidirect |
| 59. C3×3−1+2 | #41 | semidirect |
| 78. C2×C4×C9 | C2×C32 | semidirect |
| 79. #611 | C2×C32 | semidirect |
| 80. D36 | C2×C32 | semidirect |
| 81. C4×D9 | C2×C32 | semidirect |
| 82. Dic18 | C2×C32 | semidirect |
| 130. 3−1+2 | C3×#41 | semidirect |
| 132. C3×C9 | C3×#41 | semidirect |
| 143. C2×C3×C4 | AGL(1,ℤ/9) | semidirect |
| 192. C9 | C32×#41 | semidirect |
| 197. C2×C4 | C3×AGL(1,ℤ/9) | semidirect |
| 216. C3 | #3697⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×3−1+2 | 2 |
| C3×#611⋊C3 | 2 |
| C3×C4⋊AGL(1,ℤ/9) | 2 |
| C3×C4×AGL(1,ℤ/9) | 2 |
| C3×3−1+2⋊Q8 | 2 |
| C32×#235 | 3 |
| #3697⋊C3 | 3 |
| C3×#3697 | 3 |