Finite Group DatabasebetaFinite Group Databasebeta← C3×(C3×C43⋊C3)⋊C27 #44533356
Order 31347.
464 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 166 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. C32×C43⋊C27 | C3 | semidirect |
| 3. (C3×C43⋊C3)⋊C27 | C3 | direct (N × H) |
| 4. C32×C27×C43 | C3 | semidirect |
| 13. C3×C43⋊C27 | C32 | semidirect |
| 16. C3×C27×C43 | C32 | semidirect |
| 20. C32×C43⋊C3 | C27 | semidirect |
| 46. C3×C43⋊C3 | C3×C27 | semidirect |
| 54. C32×C27 | C43⋊C3 | semidirect |
| 56. C3×C43 | C32⋊C27 | semidirect |
| 73. C3×C27 | C3×C43⋊C3 | semidirect |
| 74. C43 | C3×C32⋊C27 | semidirect |
| 110. C3 | (C3×C43⋊C3)⋊C27 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C43⋊C3 | 3 |
| C32×C43⋊C27 | 3 |
| (C3×C43⋊C3)⋊C27 | 3 |
| C32×C27×C43 | 3 |
| C3×C32⋊C27 | 43 |