Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
290 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 110 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. C32×Q8×C9 | C2 | semidirect |
| 3. C3×C9×C3⋊C8 | C2 | semidirect |
| 6. C9×#215 | C3 | direct (N × H) |
| 15. C3×Q8×C9 | D3 | semidirect |
| 16. C3×Q8×C9 | C2×C3 | semidirect |
| 20. C9×C3⋊C8 | C2×C3 | semidirect |
| 24. C3×#215 | C9 | direct (N × H) |
| 40. C32×C9 | SD16 | semidirect |
| 43. C32×Q8 | C2×C9 | semidirect |
| 50. C3×C3⋊C8 | C2×C9 | semidirect |
| 53. Q8×C9 | C3×D3 | semidirect |
| 66. #215 | C3×C9 | direct (N × H) |
| 88. C3×C9 | #215 | direct (N × H) |
| 89. C3×C9 | C3×SD16 | semidirect |
| 92. C3×Q8 | D3×C9 | semidirect |
| 93. C3×Q8 | C2×C3×C9 | semidirect |
| 100. C3⋊C8 | C2×C3×C9 | semidirect |
| 128. C32 | C9×SD16 | semidirect |
| 132. C9 | C3×#215 | direct (N × H) |
| 133. Q8 | C3×D3×C9 | semidirect |
| 149. C3 | C9×#215 | direct (N × H) |
| 150. C3 | C3×C9×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×Q8×C9 | 2 |
| C3×C9×D12 | 2 |
| C3×C9×C3⋊C8 | 2 |
| C32×#215 | 3 |
| C3×C9×SD16 | 3 |
| C9×#215 | 3 |