Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
328 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 100 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. H(3,𝔽3)×C43⋊C9 | C3 | semidirect |
| 2. C3×C9×C43⋊C9 | C3 | semidirect |
| 3. H(3,𝔽3)⋊(C43⋊C9) | C3 | semidirect |
| 4. #23782716 | C3 | semidirect |
| 15. C43×#732 | C9 | semidirect |
| 26. H(3,𝔽3)×C43 | C3×C9 | semidirect |
| 29. C3×C9×C43 | C3×C9 | semidirect |
| 43. C43⋊C9 | #732 | direct (N × H) |
| 60. #732 | C43⋊C9 | direct (N × H) |
| 65. C43 | C9×#732 | semidirect |
| 69. H(3,𝔽3) | C3×C43⋊C9 | semidirect |
| 79. C3×C9 | C3×C43⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×C43⋊C9 | 3 |
| C3×C9×C43⋊C9 | 3 |
| H(3,𝔽3)⋊(C43⋊C9) | 3 |
| #23782716 | 3 |
| C3×C43×#732 | 3 |
| C9×#732 | 43 |