Finite Group DatabasebetaFinite Group DatabasebetaOrder 2187.
324 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 119 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 | C3×H(3,𝔽3) |
| commutator | C33 | C32×C9 |
| Frattini, cosocle | C32×C9 | C33 |
| socle | C32 | C3×C32⋊C9 |
| prime radical | C3×H(3,𝔽3) | C3×C9 |
| LCS | G ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C9 ◁ C3×C92 ◁ G | |
| LECS | G ▷ C32×C9 ▷ C3 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10624706 | C3 | semidirect |
| 3. C3×C9⋊C27 | C3 | semidirect |
| 5. #10624469 | C3 | semidirect |
| 94. C9 | #6872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#737 | 3 |
| #10624706 | 3 |
| C3×C9⋊C27 | 3 |
| C3×#6872 | 3 |
| #10624469 | 3 |