Finite Group DatabasebetaFinite Group DatabasebetaOrder 2187.
311 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 311 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C9 | #6895 |
| commutator | C3×C9 | C32×C9 |
| Frattini, cosocle | C32×C9 | C33 |
| socle | C3 | #10624549 |
| prime radical | C34 | H(3,𝔽3) |
| LCS | G ▷ C3×C9 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C9 ◁ C32×C9 ◁ G | |
| LECS | G ▷ C32×C9 ▷ C3 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #10624470 | C3 | semidirect |
| 11. #6887 | C9 | semidirect |
| 12. #6887 | C9 | semidirect |
| 16. C3×C9⋊C9 | C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6887 | 3 |
| #10624688 | 3 |
| #10624470 | 3 |