Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
424 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 3. C4×#1094 | C3 | direct (N × H) |
| 4. C3×C4×C22⋊C9 | C3 | semidirect |
| 5. C3×#1094 | C4 | direct (N × H) |
| 16. C4×C22⋊C9 | C32 | semidirect |
| 22. #1094 | C3×C4 | direct (N × H) |
| 23. C3×C22⋊C9 | C3×C4 | semidirect |
| 43. C22×C3×C4 | 3−1+2 | semidirect |
| 60. C22⋊C9 | C32×C4 | semidirect |
| 84. C22×C4 | C3×3−1+2 | semidirect |
| 92. C22×C3 | C4×3−1+2 | semidirect |
| 98. C3×C4 | #1094 | direct (N × H) |
| 118. C22 | C3×C4×3−1+2 | semidirect |
| 120. C4 | C3×#1094 | direct (N × H) |
| 122. C3 | C4×#1094 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1094 | 2 |
| C22×C33×C4 | 3 |
| C4×#1094 | 3 |
| C3×C4×C22⋊C9 | 3 |
| C3×C4×3−1+2 | 4 |