Finite Group DatabasebetaFinite Group DatabasebetaOrder 2916.
331 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 331 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, hypercenter | C3 | D9×(C3⋊D3)⋊C3 |
| commutator, hypocenter | C32×C9 | C22×C9 |
| Frattini, socle | C33 | C3×D32 |
| Fitting | C9×C32⋊C9 | C22 |
| prime radical | C3×D9×C3⋊D3 | C3 |
| cosocle | C33×C9 | C22×C3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×(C3⋊D3)⋊C9 | C2 | semidirect |
| 2. #13090610 | C2 | semidirect |
| 3. D9×C32⋊C9 | C2 | semidirect |
| 7. C9×C32⋊C9 | C22 | semidirect |
| 18. C3×C9×D9 | D3 | semidirect |
| 21. D9×C3⋊D3 | C9 | semidirect |
| 31. C3×C92 | C2×D3 | semidirect |
| 37. C3⋊(C3⋊D9) | C2×C9 | semidirect |
| 40. C9×C3⋊D3 | C2×C9 | semidirect |
| 54. C32×D9 | C2×C9 | semidirect |
| 62. (C3⋊D3)⋊C9 | D9 | direct (N × H) |
| 88. C32×C9 | C22×C9 | semidirect |
| 96. C32⋊C9 | C2×D9 | semidirect |
| 195. C3×C9 | D3×D9 | semidirect |
| 209. C3⋊D3 | C9×D9 | semidirect |
| 237. D9 | (C3⋊D3)⋊C9 | direct (N × H) |
| 261. C32 | C2×C9×D9 | semidirect |
| 276. C9 | C2×(C3⋊D3)⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×(C3⋊D3)⋊C9 | 2 |
| #13090610 | 2 |
| D9×C32⋊C9 | 2 |
| C3×D9×C3⋊D3 | 3 |
| D3×(C3⋊D3)⋊C9 | 3 |
| D3×C9×D9 | 3 |