Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
154 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center | C43×C81 | C32 |
| commutator | C3 | C32×C27×C43 |
| Frattini, cosocle | C27 | C33×C43 |
| socle | C3×C43 | C32×C27 |
| prime radical | H(3,𝔽3)×C43 | C27 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C43×C81 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C43×C81⋊C3 | C3 | semidirect |
| 3. C3×C43×C81 | C3 | semidirect |
| 14. #10624833 | C43 | direct (N × H) |
| 19. C81⋊C3 | C3×C43 | semidirect |
| 20. C3×C81 | C3×C43 | semidirect |
| 28. C43 | #10624833 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#6903 | 3 |
| C43×C81⋊C3 | 3 |
| C3×C43×C81 | 3 |
| #10624833 | 43 |