Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
222 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 222 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 |
|---|---|---|
| 5. #3674⋊C3 | C3 | direct (N × H) |
| 6. C3×#3674 | C3 | semidirect |
| 25. #3674 | C32 | semidirect |
| 39. C3×3−1+2 | Q16 | semidirect |
| 83. 3−1+2 | C3×Q16 | semidirect |
| 85. C3×C9 | C3×Q16 | semidirect |
| 121. C9 | C32×Q16 | semidirect |
| 134. C3 | #3674⋊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 |
| C3×3−1+2⋊Q8 | 2 |
| C3×3−1+2⋊C8 | 2 |
| C32×#216 | 3 |
| #3674⋊C3 | 3 |
| C3×#3674 | 3 |