Finite Group DatabasebetaFinite Group DatabasebetaOrder 2187.
2660 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 2660 conjugacy classes of subgroups — too many to draw. Only its 341 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C33 | C34 |
| prime radical | C3×C32⋊H(3,𝔽3) | C3 |
| LCS | G ▷ C33 ▷ C1 | |
| UCS | C1 ◁ C33 ◁ G | |
| LECS | G ▷ C33 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×#737 | C3 | semidirect |
| 2. C3×#6893 | C3 | semidirect |
| 3. C3×#6893 | C3 | semidirect |
| 4. C3×#6893 | C3 | semidirect |
| 5. C3×#6891 | C3 | semidirect |
| 7. C32×C32⋊C9 | C3 | semidirect |
| 8. #10624563 | C3 | semidirect |
| 9. #10624555 | C3 | semidirect |
| 16. C32×3−1+2 | C32 | semidirect |
| 22. C33×C9 | C32 | semidirect |
| 32. C3×C32⋊C9 | C32 | semidirect |
| 33. C3×C32⋊C9 | C32 | semidirect |
| 34. C3×C32⋊C9 | C32 | semidirect |
| 35. C3×C32⋊C9 | C32 | semidirect |
| 56. C3×3−1+2 | H(3,𝔽3) | semidirect |
| 74. C32×C9 | H(3,𝔽3) | semidirect |
| 113. C33 | #737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#737 | 3 |
| C3×#6893 | 3 |
| C3×#6891 | 3 |
| C3×C32⋊H(3,𝔽3) | 3 |
| C32×C32⋊C9 | 3 |
| #10624563 | 3 |
| #10624555 | 3 |