Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
554 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 61 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×H(3,𝔽3)×C43⋊C3 | C3 | semidirect |
| 2. #23782891 | C3 | semidirect |
| 3. #23782888 | C3 | semidirect |
| 4. #23782886 | C3 | semidirect |
| 5. #23782882 | C3 | semidirect |
| 6. #23782881 | C3 | semidirect |
| 7. C3×#16812508 | C3 | semidirect |
| 8. C3×#16812506 | C3 | semidirect |
| 9. C43×#6911 | C3 | semidirect |
| 12. C3×#11923958 | C32 | semidirect |
| 13. C3×#11923958 | C32 | semidirect |
| 14. C3×#11923958 | C32 | semidirect |
| 17. C3×C32⋊(C43⋊C3) | C32 | semidirect |
| 29. C3×3−1+2×C43 | C32 | semidirect |
| 31. C3×H(3,𝔽3)×C43 | C32 | semidirect |
| 96. #6911 | C43⋊C3 | semidirect |
| 118. C3×3−1+2 | C3×C43⋊C3 | semidirect |
| 125. C3×H(3,𝔽3) | C3×C43⋊C3 | semidirect |
| 136. C43 | #10624754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×H(3,𝔽3)×C43⋊C3 | 3 |
| #23782891 | 3 |
| #23782888 | 3 |
| #23782886 | 3 |
| #23782882 | 3 |
| #23782881 | 3 |
| C3×#16812508 | 3 |
| C3×#16812506 | 3 |
| C43×#6911 | 3 |
| #10624754 | 43 |