Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
240 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 240 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×Q8×3−1+2 | C2 | semidirect |
| 3. C3×3−1+2⋊C8 | C2 | semidirect |
| 5. #3675⋊C3 | C3 | direct (N × H) |
| 6. C3×#3675 | C3 | semidirect |
| 14. Q8×3−1+2 | C2×C3 | semidirect |
| 16. C3×Q8×C9 | C2×C3 | semidirect |
| 19. 3−1+2⋊C8 | C2×C3 | semidirect |
| 20. C3×C9⋊C8 | C2×C3 | semidirect |
| 26. #3675 | C32 | semidirect |
| 40. C3×3−1+2 | SD16 | semidirect |
| 53. Q8×C9 | C2×C32 | semidirect |
| 55. C9⋊C8 | C2×C32 | semidirect |
| 87. 3−1+2 | C3×SD16 | semidirect |
| 89. C3×C9 | C3×SD16 | semidirect |
| 92. C3×Q8 | AGL(1,ℤ/9) | semidirect |
| 129. C9 | C32×SD16 | semidirect |
| 130. Q8 | C3×AGL(1,ℤ/9) | semidirect |
| 145. C3 | #3675⋊C3 | direct (N × H) |
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 |
| C3×C4⋊AGL(1,ℤ/9) | 2 |
| C3×3−1+2⋊C8 | 2 |
| C32×#215 | 3 |
| #3675⋊C3 | 3 |
| C3×#3675 | 3 |