Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
320 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C92 | C2×C32 |
| Frattini, socle | C32 | C32×C3⋊D3 |
| Fitting | #10624899 | C2 |
| LCS | G ▷ C92 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624899 | C2 | semidirect |
| 3. #6899⋊C2 | C3 | semidirect |
| 4. #92309 | C3 | semidirect |
| 5. #92299 | C3 | semidirect |
| 6. #92299 | C3 | semidirect |
| 15. #6899 | C2×C3 | semidirect |
| 20. #6896 | C2×C3 | semidirect |
| 31. C9×3−1+2 | C2×C3 | semidirect |
| 32. C9×3−1+2 | C2×C3 | semidirect |
| 43. C9⋊D9 | C32 | semidirect |
| 128. C92 | C2×C32 | semidirect |
| 171. 3−1+2 | AGL(1,ℤ/9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624899 | 2 |
| C3×C3⋊AGL(1,ℤ/9) | 3 |
| #6899⋊C2 | 3 |
| #92309 | 3 |
| #92299 | 3 |
| #4169⋊C3 | 3 |
| C3×#4169 | 3 |