Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
196 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23782734 | C3 | semidirect |
| 4. (C43⋊C9)⋊C27 | C3 | semidirect |
| 5. (C43⋊C9)⋊C27 | C3 | semidirect |
| 7. #23782707 | C3 | semidirect |
| 8. #23782706 | C3 | semidirect |
| 9. C43×#6864 | C3 | semidirect |
| 41. C27×C43 | 3−1+2 | semidirect |
| 64. #6864 | C43⋊C3 | semidirect |
| 84. C43 | #10624727 | semidirect |
| 101. C27 | #11923956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C27×C43⋊C3 | 3 |
| C9×#11923956 | 3 |
| #23782734 | 3 |
| (C43⋊C9)⋊C27 | 3 |
| (C3×C43⋊C3)⋊C27 | 3 |
| #23782707 | 3 |
| #23782706 | 3 |
| C43×#6864 | 3 |
| #10624727 | 43 |