Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
758 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×#11923957 | C3 | semidirect |
| 3. C3×C32⋊(C43⋊C9) | C3 | semidirect |
| 4. C3×(C3×C43⋊C3)⋊C9 | C3 | semidirect |
| 5. C3×(C3×C43⋊C3)⋊C9 | C3 | semidirect |
| 6. C3×(C3×C43⋊C3)⋊C9 | C3 | semidirect |
| 7. C3×C43×C32⋊C9 | C3 | semidirect |
| 41. C32×C43⋊C3 | 3−1+2 | semidirect |
| 51. C3×C43⋊C9 | H(3,𝔽3) | semidirect |
| 58. C33×C43 | 3−1+2 | semidirect |
| 65. C3×C9×C43 | H(3,𝔽3) | semidirect |
| 107. C3×C32⋊C9 | C43⋊C3 | semidirect |
| 136. C43 | #10624563 | semidirect |
| 159. C33 | #11923957 | semidirect |
| 176. C3×C9 | C32⋊(C43⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11923957 | 3 |
| C32×C32⋊(C43⋊C3) | 3 |
| C3×C32⋊(C43⋊C9) | 3 |
| C3×(C3×C43⋊C3)⋊C9 | 3 |
| C3×C43×C32⋊C9 | 3 |
| #10624563 | 43 |