Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
263 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 263 conjugacy classes of subgroups — too many to draw. Only its 51 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 | #4207⋊C3 |
| commutator, cosocle | C32×C9 | C2×C32 |
| Frattini, socle | C32 | C32×C3⋊D3 |
| Fitting | #10624887 | C2 |
| prime radical | C3×#4207 | C3 |
| hypocenter | C3×C9 | C2×3−1+2 |
| LCS | G ▷ C32×C9 ▷ C3×C9 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624887 | C2 | semidirect |
| 3. #92294 | C3 | semidirect |
| 4. #92294 | C3 | semidirect |
| 5. C3⋊(D9⋊C9) | C3 | semidirect |
| 12. #6900 | D3 | semidirect |
| 20. #6896 | D3 | semidirect |
| 28. #6894 | D3 | semidirect |
| 31. #6887 | C2×C3 | semidirect |
| 32. #6887 | C2×C3 | semidirect |
| 33. C3×C9⋊C9 | C2×C3 | semidirect |
| 135. C3⋊D9 | 3−1+2 | semidirect |
| 192. C3×C9 | C2×3−1+2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624887 | 2 |
| C3×#4207 | 3 |
| #92294 | 3 |
| C3⋊(D9⋊C9) | 3 |
| #92265 | 3 |
| #92264 | 3 |
| #6894⋊C2 | 3 |
| #92262 | 3 |