Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
368 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 112 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. #23782782 | C3 | semidirect |
| 3. #23782724 | C3 | semidirect |
| 5. C3×C92×C43 | C3 | semidirect |
| 8. #16812525 | C9 | semidirect |
| 60. C3×C92 | C43⋊C3 | semidirect |
| 86. C43 | #10624697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812525 | 3 |
| #23782782 | 3 |
| #23782724 | 3 |
| #23782721 | 3 |
| C3×C92×C43 | 3 |
| #10624697 | 43 |