Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
254 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 70 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×Q8×3−1+2 | C2 | semidirect |
| 3. C3⋊(3−1+2⋊C8) | C2 | semidirect |
| 5. #88548 | C3 | semidirect |
| 14. Q8×3−1+2 | D3 | semidirect |
| 16. C3×Q8×C9 | C2×C3 | semidirect |
| 19. C3⋊(C9⋊C8) | C2×C3 | semidirect |
| 40. C3×3−1+2 | SD16 | semidirect |
| 52. Q8×C9 | C3×D3 | semidirect |
| 84. 3−1+2 | #215 | semidirect |
| 86. C3×C9 | C3×SD16 | semidirect |
| 89. C3×Q8 | AGL(1,ℤ/9) | semidirect |
| 124. C9 | C3×#215 | semidirect |
| 125. Q8 | C3⋊AGL(1,ℤ/9) | semidirect |
| 140. C3 | #3675⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×3−1+2 | 2 |
| C4⋊(C3⋊AGL(1,ℤ/9)) | 2 |
| C3⋊(3−1+2⋊C8) | 2 |
| C3×#3755 | 3 |
| #88548 | 3 |
| #3675⋊C3 | 3 |