Finite Group DatabasebetaFinite Group DatabasebetaOrder 2187.
3464 conjugacy classes of subgroups; only the 1412 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 1412 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C33×C9 | C32 |
| commutator | C3 | C32×C92 |
| Frattini, cosocle | C33 | C34 |
| socle | C34 | C33 |
| prime radical | C35 | C32 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C33×C9 ◁ G | |
| LECS | G ▷ C33 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C32×C92 | C3 | semidirect |
| 4. C9×C32⋊C9 | C3 | direct (N × H) |
| 5. C3×#6855 | C3 | semidirect |
| 9. C33×C9 | C9 | semidirect |
| 14. C3×C32⋊C9 | C9 | direct (N × H) |
| 17. C3×C92 | C32 | semidirect |
| 18. #6855 | C32 | semidirect |
| 35. C32×C9 | C3×C9 | semidirect |
| 36. C32×C9 | C3×C9 | semidirect |
| 42. C32⋊C9 | C3×C9 | direct (N × H) |
| 51. C33 | C92 | semidirect |
| 67. C3×C9 | C32⋊C9 | direct (N × H) |
| 70. C3×C9 | C32×C9 | semidirect |
| 79. C32 | C3×C92 | semidirect |
| 91. C9 | C3×C32⋊C9 | direct (N × H) |
| 93. C3 | C9×C32⋊C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C34×C9 | 3 |
| C32×C32⋊C9 | 3 |
| C32×C92 | 3 |
| C9×C32⋊C9 | 3 |
| C3×#6855 | 3 |