Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
728 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 292 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. #23782820 | C3 | semidirect |
| 3. #23782818 | C3 | semidirect |
| 4. #23782815 | C3 | semidirect |
| 12. #16812499 | C32 | semidirect |
| 13. (C43⋊C9)⋊C9 | C32 | semidirect |
| 77. C43 | #10624886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11923958 | 3 |
| #23782820 | 3 |
| #23782818 | 3 |
| #23782815 | 3 |
| C3×C32⋊(C43⋊C9) | 3 |
| C3×C43×C32⋊C9 | 3 |
| #10624886 | 43 |