Finite Group DatabasebetaFinite Group DatabasebetaOrder 2187.
196 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C3×C9 | #732 |
| commutator, Frattini, cosocle | C32×C9 | C33 |
| socle | C32 | C3×#732 |
| prime radical | C33 | C3×H(3,𝔽3) |
| LCS | G ▷ C32×C9 ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C9 ◁ C32×C9 ◁ C3×C92 ◁ G | |
| LECS | G ▷ C32×C9 ▷ C33 ▷ C3 ▷ C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#733 | 3 |
| C9×C9⋊C9 | 3 |
| #10624494 | 3 |
| #10624493 | 3 |
| #10624491 | 3 |
| #10624490 | 3 |
| #10624483 | 3 |
| #10624482 | 3 |