Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
268 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 64 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. #23782800 | C3 | semidirect |
| 2. H(3,𝔽3)×C43⋊C9 | C3 | semidirect |
| 3. C3×(C43⋊C9)⋊C9 | C3 | semidirect |
| 4. H(3,𝔽3)⋊(C43⋊C9) | C3 | semidirect |
| 5. H(3,𝔽3)⋊(C43⋊C9) | C3 | semidirect |
| 6. H(3,𝔽3)⋊(C43⋊C9) | C3 | semidirect |
| 7. H(3,𝔽3)⋊(C43⋊C9) | C3 | semidirect |
| 8. #23782716 | C3 | semidirect |
| 44. H(3,𝔽3)×C43 | 3−1+2 | semidirect |
| 70. C43⋊C9 | #732 | semidirect |
| 104. C43 | #10624792 | semidirect |
| 112. H(3,𝔽3) | #11923958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782800 | 3 |
| H(3,𝔽3)×C43⋊C9 | 3 |
| C3×(C43⋊C9)⋊C9 | 3 |
| H(3,𝔽3)⋊(C43⋊C9) | 3 |
| #23782716 | 3 |
| C3×C43×#732 | 3 |
| #10624792 | 43 |