Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
274 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 14. #16812514 | C9 | direct (N × H) |
| 58. C9×C43 | #733 | semidirect |
| 97. C43 | C9×#733 | semidirect |
| 133. C9 | #16812514 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812514 | 3 |
| C9×#11923958 | 3 |
| C3×C9×C43⋊C9 | 3 |
| #23782725 | 3 |
| 3−1+2⋊(C43⋊C9) | 3 |
| #23782722 | 3 |
| #23782715 | 3 |
| C9×3−1+2×C43 | 3 |
| C9×#733 | 43 |