Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
362 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 362 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. #23782715 | C3 | semidirect |
| 4. #23782713 | C3 | semidirect |
| 6. C43×#6887 | C3 | semidirect |
| 12. C3×#11923956 | C9 | semidirect |
| 65. #6887 | C43⋊C3 | semidirect |
| 91. C43 | #10624692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11923956 | 3 |
| #23782782 | 3 |
| #23782715 | 3 |
| #23782713 | 3 |
| #23782711 | 3 |
| C43×#6887 | 3 |
| #10624692 | 43 |