Finite Group DatabasebetaFinite Group DatabasebetaOrder 2187.
2348 conjugacy classes of subgroups; only the 548 normal subgroups are shown.
This group has 2348 conjugacy classes of subgroups — too many to draw. Only its 548 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C34 | C33 |
| commutator, Frattini, cosocle | C33 | C34 |
| prime radical | C35 | C32 |
| LCS | G ▷ C33 ▷ C1 | |
| UCS | C1 ◁ C34 ◁ G | |
| LECS | G ▷ C33 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C32×C9⋊C9 | C3 | semidirect |
| 4. #10624565 | C3 | direct (N × H) |
| 5. C3×#6855 | C3 | semidirect |
| 6. C3×#6855 | C3 | semidirect |
| 7. C3×#6855 | C3 | semidirect |
| 20. C3×C9⋊C9 | C32 | semidirect |
| 23. #6855 | C32 | semidirect |
| 24. #6855 | C32 | semidirect |
| 25. #6855 | C32 | semidirect |
| 56. C32×C9 | 3−1+2 | semidirect |
| 106. C3×C9 | C3×3−1+2 | semidirect |
| 132. C3 | #10624565 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×3−1+2 | 3 |
| C32×C9⋊C9 | 3 |
| C32×C32⋊C9 | 3 |
| #10624565 | 3 |
| C3×#6855 | 3 |