Finite Group DatabasebetaFinite Group DatabasebetaOrder 2187.
428 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C32×C9 | C33 |
| commutator | C32 | C32×C27 |
| socle | C33 | C32×C9 |
| prime radical | C34 | C3×C9 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C9 ◁ G | |
| LECS | G ▷ C32×C9 ▷ C3 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C9⋊C27 | C3 | semidirect |
| 5. #10624463 | C3 | semidirect |
| 42. C32⋊C9 | C27 | semidirect |
| 65. C3×C9 | C3×C27 | semidirect |
| 81. C32 | C9⋊C27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C27 | 3 |
| C3×C9⋊C27 | 3 |
| C3×C32⋊C27 | 3 |
| C9×C32⋊C9 | 3 |
| #10624463 | 3 |