Finite Group DatabasebetaFinite Group DatabasebetaOrder 2187.
1976 conjugacy classes of subgroups; only the 350 normal subgroups are shown.
This group has 1976 conjugacy classes of subgroups — too many to draw. Only its 350 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C33 | C34 |
| prime radical | C35 | C32 |
| LCS | G ▷ C33 ▷ C1 | |
| UCS | C1 ◁ C33 ◁ G | |
| LECS | G ▷ C33 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #10624570 | C3 | semidirect |
| 6. #10624567 | C3 | semidirect |
| 7. #10624558 | C3 | semidirect |
| 8. #10624558 | C3 | semidirect |
| 31. #6855 | C32 | semidirect |
| 52. C3×3−1+2 | 3−1+2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×3−1+2 | 3 |
| C3×#6891 | 3 |
| C32×C32⋊C9 | 3 |
| #10624570 | 3 |
| #10624567 | 3 |
| #10624558 | 3 |