Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
328 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C3×C9×C43 | H(3,𝔽3) |
| commutator | C32 | C32×C9×C43 |
| Frattini, cosocle | C33 | C33×C43 |
| socle | C32×C43 | C3×H(3,𝔽3) |
| prime radical | C3×C43×#732 | C3 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C9×C43 ◁ C32×C9×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C9×H(3,𝔽3)×C43 | C3 | semidirect |
| 3. C3×C92×C43 | C3 | semidirect |
| 4. C43×H(3,𝔽3)⋊C9 | C3 | semidirect |
| 5. C43×#6868 | C3 | semidirect |
| 11. C43×#732 | C9 | direct (N × H) |
| 19. H(3,𝔽3)×C43 | C3×C9 | semidirect |
| 27. C3×C9×C43 | C3×C9 | semidirect |
| 30. C9×#732 | C43 | direct (N × H) |
| 43. C9×C43 | #732 | direct (N × H) |
| 45. C9×H(3,𝔽3) | C3×C43 | semidirect |
| 46. C3×C92 | C3×C43 | semidirect |
| 47. H(3,𝔽3)⋊C9 | C3×C43 | semidirect |
| 48. #6868 | C3×C43 | semidirect |
| 60. #732 | C9×C43 | direct (N × H) |
| 65. C43 | C9×#732 | direct (N × H) |
| 69. H(3,𝔽3) | C3×C9×C43 | semidirect |
| 77. C3×C9 | C3×C9×C43 | semidirect |
| 92. C9 | C43×#732 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C43×#732 | 3 |
| C9×H(3,𝔽3)×C43 | 3 |
| C3×C92×C43 | 3 |
| C43×H(3,𝔽3)⋊C9 | 3 |
| C43×#6868 | 3 |
| C9×#732 | 43 |