Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
434 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C9 | H(3,𝔽3) |
| commutator | C32 | C2×C32×C9 |
| Frattini, cosocle | C33 | C2×C33 |
| socle | C2×C32 | C3×H(3,𝔽3) |
| prime radical | C2×C34 | C32 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C9 ◁ C2×C32×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624688 | C2 | direct (N × H) |
| 3. C2×#6887 | C3 | semidirect |
| 4. C2×#6868 | C3 | semidirect |
| 5. C2×#6867 | C3 | semidirect |
| 8. #6887 | C2×C3 | semidirect |
| 9. #6868 | C2×C3 | semidirect |
| 10. #6867 | C2×C3 | semidirect |
| 16. C2×C32×C9 | C9 | semidirect |
| 27. C32×C9 | C2×C9 | semidirect |
| 106. C2 | #10624688 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624688 | 2 |
| C2×C33×C9 | 3 |
| C2×#6887 | 3 |
| C2×#6868 | 3 |
| C2×#6867 | 3 |
| C2×#6866 | 3 |