Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
692 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 70 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. C3×H(3,𝔽3)×C43⋊C3 | C3 | semidirect |
| 2. C32⋊C9×C43⋊C3 | C3 | semidirect |
| 3. #23782687 | C3 | semidirect |
| 4. #23782686 | C3 | semidirect |
| 5. C43×#6856 | C3 | semidirect |
| 9. C3×C32⋊(C43⋊C3) | C32 | semidirect |
| 12. C32⋊(C43⋊C9) | C32 | semidirect |
| 14. C3×H(3,𝔽3)×C43 | C32 | semidirect |
| 15. C43×C32⋊C9 | C32 | semidirect |
| 54. #6856 | C43⋊C3 | direct (N × H) |
| 61. C43⋊C3 | #6856 | direct (N × H) |
| 67. C3×H(3,𝔽3) | C3×C43⋊C3 | semidirect |
| 71. C32⋊C9 | C3×C43⋊C3 | semidirect |
| 72. C43 | C3×#6856 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×H(3,𝔽3)×C43⋊C3 | 3 |
| C32⋊C9×C43⋊C3 | 3 |
| #23782687 | 3 |
| #23782686 | 3 |
| C43×#6856 | 3 |
| C3×#6856 | 43 |