Finite Group DatabasebetaFinite Group DatabasebetaOrder 2187.
2156 conjugacy classes of subgroups; only the 638 normal subgroups are shown.
This group has 2156 conjugacy classes of subgroups — too many to draw. Only its 638 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, cosocle | C33 | C34 |
| commutator | C32 | C33×C9 |
| prime radical | C35 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C33 ◁ G | |
| LECS | G ▷ C33 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C9×3−1+2 | C3 | semidirect |
| 4. #10624560 | C3 | semidirect |
| 5. #10624558 | C3 | semidirect |
| 6. #10624548 | C3 | semidirect |
| 8. C9×C32⋊C9 | C3 | semidirect |
| 12. C32×3−1+2 | C9 | semidirect |
| 19. C3×C9⋊C9 | C32 | semidirect |
| 27. C3×C92 | C32 | semidirect |
| 28. #6855 | C32 | semidirect |
| 29. #6855 | C32 | semidirect |
| 48. C3×3−1+2 | C3×C9 | semidirect |
| 56. C32×C9 | C3×C9 | semidirect |
| 68. C32⋊C9 | 3−1+2 | direct (N × H) |
| 103. 3−1+2 | C32⋊C9 | direct (N × H) |
| 120. C3×C9 | C3×3−1+2 | semidirect |
| 144. C32 | C9×3−1+2 | semidirect |
| 156. C9 | C3×C32⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×3−1+2 | 3 |
| C3×C9×3−1+2 | 3 |
| C32×C32⋊C9 | 3 |
| #10624560 | 3 |
| #10624558 | 3 |
| #10624548 | 3 |
| #10624547 | 3 |
| C9×C32⋊C9 | 3 |