Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
192 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 192 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 |
|---|---|---|
| 2. (C43⋊C9)⋊C27 | C3 | semidirect |
| 3. (C43⋊C9)⋊C27 | C3 | semidirect |
| 4. (C43⋊C9)⋊C27 | C3 | semidirect |
| 6. #23782707 | C3 | semidirect |
| 7. #23782706 | C3 | semidirect |
| 8. C27×C43⋊C9 | C3 | semidirect |
| 41. C27×C43 | 3−1+2 | semidirect |
| 55. C43⋊C9 | C27⋊C3 | semidirect |
| 84. C43 | #10624728 | semidirect |
| 101. C27 | #11923958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#11923958 | 3 |
| (C43⋊C9)⋊C27 | 3 |
| C32⋊(C43⋊C27) | 3 |
| #23782707 | 3 |
| #23782706 | 3 |
| C27×C43⋊C9 | 3 |
| C3×C43×C27⋊C3 | 3 |
| #10624728 | 43 |