Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
230 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 2. #23782734 | C3 | semidirect |
| 3. #23782733 | C3 | semidirect |
| 4. (C43⋊C9)⋊C27 | C3 | semidirect |
| 6. C27×C43⋊C9 | C3 | semidirect |
| 7. C43×C9⋊C27 | C3 | semidirect |
| 28. C9×C43⋊C3 | C27 | semidirect |
| 52. C9⋊C27 | C43⋊C3 | semidirect |
| 71. C43 | #10624710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C92×C43⋊C3 | 3 |
| #23782734 | 3 |
| #23782733 | 3 |
| (C43⋊C9)⋊C27 | 3 |
| (C3×C43⋊C3)⋊C27 | 3 |
| C27×C43⋊C9 | 3 |
| C43×C9⋊C27 | 3 |
| #10624710 | 43 |