Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
1754 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 1754 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #4207 |
| commutator, cosocle, hypocenter | C3×C9 | C2×C33 |
| Frattini | C3 | C33×C3⋊D3 |
| Fitting | C32×#737 | C2 |
| socle | C33 | C3×C3⋊D3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×#737 | C2 | semidirect |
| 2. C3×#4207 | C3 | direct (N × H) |
| 3. C32×C3⋊D9 | C3 | semidirect |
| 10. C3×#737 | C2×C3 | semidirect |
| 13. C32×3−1+2 | D3 | semidirect |
| 16. C33×C9 | D3 | semidirect |
| 17. C33×C9 | C2×C3 | semidirect |
| 20. #4207 | C32 | direct (N × H) |
| 21. C3×C3⋊D9 | C32 | semidirect |
| 34. #737 | C2×C32 | semidirect |
| 40. C3×3−1+2 | C3×D3 | semidirect |
| 53. C32×C9 | C3×D3 | semidirect |
| 54. C32×C9 | C2×C32 | semidirect |
| 60. C3⋊D9 | C33 | semidirect |
| 82. 3−1+2 | C32×D3 | semidirect |
| 98. C3×C9 | C32×D3 | semidirect |
| 99. C3×C9 | C2×C33 | semidirect |
| 119. C32 | #4207 | direct (N × H) |
| 138. C3 | C3×#4207 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#737 | 2 |
| C3×#4207 | 3 |
| C32×C3⋊D9 | 3 |
| C32×AGL(1,ℤ/9) | 3 |
| C32×(C3⋊D3)⋊C3 | 3 |
| C33×D9 | 3 |