Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
192 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 3. #23782733 | C3 | semidirect |
| 4. (C43⋊C9)⋊C27 | C3 | semidirect |
| 6. #23782707 | C3 | semidirect |
| 7. C9×C27×C43 | C3 | semidirect |
| 33. C27×C43 | 3−1+2 | semidirect |
| 40. C9×C43 | C27⋊C3 | semidirect |
| 52. C9×C27 | C43⋊C3 | semidirect |
| 69. C43 | #10624728 | semidirect |
| 83. C27 | #11923957 | semidirect |
| 92. C9 | #16812504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812504 | 3 |
| C9×#11923957 | 3 |
| #23782733 | 3 |
| (C43⋊C9)⋊C27 | 3 |
| (C3×C43⋊C3)⋊C27 | 3 |
| #23782707 | 3 |
| C9×C27×C43 | 3 |
| #10624728 | 43 |