Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
276 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 86 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 | C3×C43×AΣL(1,𝔽27) | C3 |
| 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×#6894 | C3 | semidirect |
| 3. C9×H(3,𝔽3)×C43 | C3 | semidirect |
| 4. C3×C43×C32⋊C9 | C3 | semidirect |
| 5. C43×3−1+2⋊C9 | C3 | semidirect |
| 6. C43×3−1+2⋊C9 | C3 | semidirect |
| 7. C43×H(3,𝔽3)⋊C9 | C3 | semidirect |
| 8. C43×H(3,𝔽3)⋊C9 | C3 | semidirect |
| 9. C43×#6866 | C3 | semidirect |
| 50. #10624797 | C43 | direct (N × H) |
| 76. #6894 | C3×C43 | semidirect |
| 77. C9×H(3,𝔽3) | C3×C43 | semidirect |
| 78. C3×C32⋊C9 | C3×C43 | semidirect |
| 79. 3−1+2⋊C9 | C3×C43 | semidirect |
| 80. 3−1+2⋊C9 | C3×C43 | semidirect |
| 81. H(3,𝔽3)⋊C9 | C3×C43 | semidirect |
| 82. H(3,𝔽3)⋊C9 | C3×C43 | semidirect |
| 83. #6866 | C3×C43 | semidirect |
| 108. C43 | #10624797 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C43×AΣL(1,𝔽27) | 3 |
| C43×#6894 | 3 |
| C9×H(3,𝔽3)×C43 | 3 |
| C3×C43×C32⋊C9 | 3 |
| C43×3−1+2⋊C9 | 3 |
| C43×H(3,𝔽3)⋊C9 | 3 |
| C43×#6866 | 3 |
| #10624797 | 43 |