Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
320 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 49 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. #23782797 | C3 | semidirect |
| 2. #23782796 | C3 | semidirect |
| 3. (C3×C43⋊C3)⋊H(3,𝔽3) | C3 | semidirect |
| 4. (C3×C43⋊C3)⋊H(3,𝔽3) | C3 | semidirect |
| 5. #23782687 | C3 | semidirect |
| 6. #23782687 | C3 | semidirect |
| 7. #23782686 | C3 | semidirect |
| 8. #23782686 | C3 | semidirect |
| 9. C43×#6856 | C3 | semidirect |
| 106. #6856 | C43⋊C3 | semidirect |
| 140. C43 | #10624656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782797 | 3 |
| #23782796 | 3 |
| (C3×C43⋊C3)⋊H(3,𝔽3) | 3 |
| #23782687 | 3 |
| #23782686 | 3 |
| C43×#6856 | 3 |
| #10624656 | 43 |