Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
230 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 112 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. (C43⋊C9)⋊C27 | C3 | semidirect |
| 4. C9×C43⋊C27 | C3 | semidirect |
| 5. C9×C27×C43 | C3 | semidirect |
| 25. C9×C43⋊C3 | C27 | semidirect |
| 50. C9×C27 | C43⋊C3 | semidirect |
| 67. 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 |
| (C43⋊C9)⋊C27 | 3 |
| (C3×C43⋊C3)⋊C27 | 3 |
| C9×C43⋊C27 | 3 |
| C9×C27×C43 | 3 |
| #10624710 | 43 |