Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
144 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 52 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. C32×C43⋊C27 | C3 | semidirect |
| 2. C32⋊(C43⋊C27) | C3 | semidirect |
| 17. H(3,𝔽3)×C43 | C27 | semidirect |
| 61. C43 | H(3,𝔽3)⋊C27 | semidirect |
| 65. H(3,𝔽3) | C43⋊C27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C43⋊C27 | 3 |
| C32⋊(C43⋊C27) | 3 |
| C9×H(3,𝔽3)×C43 | 3 |
| H(3,𝔽3)⋊C27 | 43 |