Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
344 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 130 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 |
|---|---|---|
| 1. #23782782 | C3 | semidirect |
| 2. C3×#16812500 | C3 | semidirect |
| 3. 3−1+2⋊(C43⋊C9) | C3 | semidirect |
| 14. C43×#737 | C9 | semidirect |
| 59. #737 | C43⋊C9 | semidirect |
| 72. C43 | #10624700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782782 | 3 |
| C3×#16812500 | 3 |
| 3−1+2⋊(C43⋊C9) | 3 |
| H(3,𝔽3)⋊(C43⋊C9) | 3 |
| C3×C43×#737 | 3 |
| #10624700 | 43 |