Finite Group DatabasebetaFinite Group DatabasebetaOrder 2187.
234 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C32 | #6895 |
| commutator, Frattini, cosocle | C32×C9 | C33 |
| prime radical | C34 | 3−1+2 |
| LCS | G ▷ C32×C9 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32 ◁ C32×C9 ◁ G | |
| LECS | G ▷ C32×C9 ▷ C3 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#6875 | C3 | semidirect |
| 2. C3×#6875 | C3 | semidirect |
| 6. #10624472 | C3 | semidirect |
| 7. #10624472 | C3 | semidirect |
| 8. #10624472 | C3 | semidirect |
| 9. #10624472 | C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6875 | 3 |
| C3×#6869 | 3 |
| #10624548 | 3 |
| #10624472 | 3 |