Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
842 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 842 conjugacy classes of subgroups — too many to draw. Only its 206 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C33×C43 | C33 |
| commutator | C32 | C32×C9×C43 |
| Frattini, cosocle | C33 | C33×C43 |
| prime radical | C32×H(3,𝔽3)×C43 | C3 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C33×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C33×C9×C43 | C3 | semidirect |
| 3. C3×C43×C32⋊C9 | C3 | semidirect |
| 4. C3×C43×C32⋊C9 | C3 | semidirect |
| 9. C3×H(3,𝔽3)×C43 | C9 | semidirect |
| 23. C33×C43 | C3×C9 | semidirect |
| 33. C3×C9×C43 | H(3,𝔽3) | semidirect |
| 34. #10624555 | C43 | direct (N × H) |
| 44. C32×C43 | C32⋊C9 | semidirect |
| 53. C33×C9 | C3×C43 | semidirect |
| 54. C3×C32⋊C9 | C3×C43 | semidirect |
| 55. C3×C32⋊C9 | C3×C43 | semidirect |
| 67. C3×H(3,𝔽3) | C9×C43 | semidirect |
| 74. C43 | #10624555 | direct (N × H) |
| 82. C33 | C3×C9×C43 | semidirect |
| 92. C3×C9 | H(3,𝔽3)×C43 | semidirect |
| 102. C32 | C43×C32⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×H(3,𝔽3)×C43 | 3 |
| C33×C9×C43 | 3 |
| C3×C43×C32⋊C9 | 3 |
| #10624555 | 43 |