Finite Group DatabasebetaFinite Group DatabasebetaOrder 2187.
1313 conjugacy classes of subgroups; only the 323 normal subgroups are shown.
This group has 1313 conjugacy classes of subgroups — too many to draw. Only its 323 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 |
|---|---|---|
| 1. C3×#6896 | C3 | semidirect |
| 4. #10624567 | C3 | semidirect |
| 5. #10624566 | C3 | semidirect |
| 6. #10624557 | C3 | semidirect |
| 7. #10624556 | C3 | semidirect |
| 8. #10624556 | C3 | semidirect |
| 9. #10624548 | C3 | semidirect |
| 11. C9×C32⋊C9 | C3 | semidirect |
| 18. C3×C9⋊C9 | C32 | semidirect |
| 19. C3×C9⋊C9 | C32 | semidirect |
| 20. C3×C9⋊C9 | C32 | semidirect |
| 33. C3×C92 | C32 | semidirect |
| 34. #6855 | C32 | semidirect |
| 35. #6855 | C32 | semidirect |
| 36. #6855 | C32 | semidirect |
| 37. #6855 | C32 | semidirect |
| 78. C32⋊C9 | 3−1+2 | semidirect |
| 161. C32 | #6896 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6896 | 3 |
| C3×#6891 | 3 |
| C32×C32⋊C9 | 3 |
| #10624567 | 3 |
| #10624566 | 3 |
| #10624557 | 3 |
| #10624556 | 3 |
| #10624548 | 3 |
| #10624547 | 3 |
| C9×C32⋊C9 | 3 |