Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
260 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 260 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 |
|---|---|---|
| 2. C3×3−1+2⋊Q8 | C2 | semidirect |
| 3. C3×3−1+2⋊C8 | C2 | semidirect |
| 5. #3672⋊C3 | C3 | direct (N × H) |
| 6. C3×#3672 | C3 | semidirect |
| 17. 3−1+2⋊Q8 | C2×C3 | semidirect |
| 18. C3×Dic18 | C2×C3 | semidirect |
| 19. 3−1+2⋊C8 | C2×C3 | semidirect |
| 20. C3×C9⋊C8 | C2×C3 | semidirect |
| 26. #3672 | C32 | semidirect |
| 40. C3×3−1+2 | SD16 | semidirect |
| 54. Dic18 | C2×C32 | semidirect |
| 55. C9⋊C8 | C2×C32 | semidirect |
| 89. 3−1+2 | C3×SD16 | semidirect |
| 91. C3×C9 | C3×SD16 | semidirect |
| 134. C9 | C32×SD16 | semidirect |
| 151. C3 | #3672⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×3−1+2 | 2 |
| C3×3−1+2⋊Q8 | 2 |
| C3×3−1+2⋊C8 | 2 |
| C32×#214 | 3 |
| #3672⋊C3 | 3 |
| C3×#3672 | 3 |