Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
692 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 94 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×C32⋊(C43⋊C3) | C3 | semidirect |
| 2. C3×C32⋊(C43⋊C9) | C3 | semidirect |
| 3. #23782686 | C3 | direct (N × H) |
| 4. C32×H(3,𝔽3)×C43 | C3 | semidirect |
| 8. C3×C32⋊(C43⋊C3) | C32 | semidirect |
| 11. C32⋊(C43⋊C9) | C32 | semidirect |
| 16. C3×H(3,𝔽3)×C43 | C32 | semidirect |
| 59. C32×H(3,𝔽3) | C43⋊C3 | semidirect |
| 65. C3×C43 | #6856 | semidirect |
| 78. C3×H(3,𝔽3) | C3×C43⋊C3 | semidirect |
| 82. C43 | C3×#6856 | semidirect |
| 127. C3 | #23782686 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C32⋊(C43⋊C3) | 3 |
| C3×C32⋊(C43⋊C9) | 3 |
| #23782686 | 3 |
| C32×H(3,𝔽3)×C43 | 3 |
| C3×#6856 | 43 |