Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
278 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 74 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×D4×3−1+2 | C2 | semidirect |
| 2. C3×C4⋊AGL(1,ℤ/9) | C2 | semidirect |
| 3. C3×3−1+2⋊C8 | C2 | semidirect |
| 5. #3673⋊C3 | C3 | direct (N × H) |
| 6. C3×#3673 | C3 | semidirect |
| 14. D4×3−1+2 | C2×C3 | semidirect |
| 16. C3×D4×C9 | C2×C3 | semidirect |
| 17. C4⋊AGL(1,ℤ/9) | C2×C3 | semidirect |
| 18. C3×D36 | C2×C3 | semidirect |
| 19. 3−1+2⋊C8 | C2×C3 | semidirect |
| 20. C3×C9⋊C8 | C2×C3 | semidirect |
| 27. #3673 | C32 | semidirect |
| 41. C3×3−1+2 | D8 | semidirect |
| 54. D4×C9 | C2×C32 | semidirect |
| 55. D36 | C2×C32 | semidirect |
| 56. C9⋊C8 | C2×C32 | semidirect |
| 93. 3−1+2 | C3×D8 | semidirect |
| 95. C3×C9 | C3×D8 | semidirect |
| 100. C3×D4 | AGL(1,ℤ/9) | semidirect |
| 142. C9 | C32×D8 | semidirect |
| 144. D4 | C3×AGL(1,ℤ/9) | semidirect |
| 162. C3 | #3673⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×3−1+2 | 2 |
| C3×C4⋊AGL(1,ℤ/9) | 2 |
| C3×3−1+2⋊C8 | 2 |
| C32×#213 | 3 |
| #3673⋊C3 | 3 |
| C3×#3673 | 3 |