Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
326 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C43 | C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C43 |
| prime radical | C34×C43 | C32 |
| LCS | G ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C43 ◁ C32×C9×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C43×#6895 | C3 | semidirect |
| 3. C43×#6868 | C3 | semidirect |
| 4. C43×#6867 | C3 | semidirect |
| 36. #10624770 | C43 | direct (N × H) |
| 52. #6895 | C3×C43 | semidirect |
| 53. #6868 | C3×C43 | semidirect |
| 54. #6867 | C3×C43 | semidirect |
| 72. C43 | #10624770 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×3−1+2×C43 | 3 |
| C43×#6895 | 3 |
| C43×#6868 | 3 |
| C43×#6867 | 3 |
| C43×#6866 | 3 |
| #10624770 | 43 |