Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
276 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 90 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. C32×C9⋊C8 | C2 | semidirect |
| 5. C3×#3675 | C3 | direct (N × H) |
| 13. C3×Q8×C9 | C2×C3 | semidirect |
| 15. C3×C9⋊C8 | C2×C3 | semidirect |
| 20. #3675 | C32 | direct (N × H) |
| 29. C32×C9 | SD16 | semidirect |
| 31. C32×Q8 | D9 | semidirect |
| 38. Q8×C9 | C2×C32 | semidirect |
| 40. C9⋊C8 | C2×C32 | semidirect |
| 63. C3×C9 | C3×SD16 | semidirect |
| 65. C3×Q8 | C3×D9 | semidirect |
| 89. C32 | #3675 | direct (N × H) |
| 92. C9 | C32×SD16 | semidirect |
| 93. Q8 | C32×D9 | semidirect |
| 105. C3 | C3×#3675 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×Q8×C9 | 2 |
| C32×D36 | 2 |
| C32×C9⋊C8 | 2 |
| C32×#215 | 3 |
| C3×#3675 | 3 |