Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
318 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 58 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. C3×#16812525 | C3 | semidirect |
| 2. #23782815 | C3 | semidirect |
| 3. #23782699 | C3 | semidirect |
| 4. #23782696 | C3 | semidirect |
| 5. #23782692 | C3 | semidirect |
| 6. #23782690 | C3 | semidirect |
| 7. #23782689 | C3 | semidirect |
| 9. C9×H(3,𝔽3)×C43 | C3 | semidirect |
| 72. C9×H(3,𝔽3) | C43⋊C3 | semidirect |
| 104. C43 | #10624595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812525 | 3 |
| #23782815 | 3 |
| #23782699 | 3 |
| #23782696 | 3 |
| #23782692 | 3 |
| #23782690 | 3 |
| #23782689 | 3 |
| #23782686 | 3 |
| C9×H(3,𝔽3)×C43 | 3 |
| #10624595 | 43 |