Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1082 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 280 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. C32×#11923958 | C3 | semidirect |
| 3. #23782808 | C3 | semidirect |
| 4. #23782805 | C3 | semidirect |
| 5. #23782804 | C3 | semidirect |
| 6. #23782801 | C3 | semidirect |
| 7. #23782798 | C3 | semidirect |
| 9. #23782783 | C3 | semidirect |
| 10. C3×C43×C32⋊C9 | C3 | semidirect |
| 17. C3×#11923957 | C32 | semidirect |
| 18. C3×#11923956 | C32 | semidirect |
| 23. C3×C9×C43⋊C3 | C32 | semidirect |
| 26. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 27. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 28. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 39. #11923958 | H(3,𝔽3) | semidirect |
| 71. C32×C43 | #737 | semidirect |
| 91. C3×C32⋊C9 | C43⋊C3 | semidirect |
| 123. C43 | #10624896 | semidirect |
| 162. C32 | #16812525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812525 | 3 |
| C32×#11923958 | 3 |
| #23782808 | 3 |
| #23782805 | 3 |
| #23782804 | 3 |
| #23782801 | 3 |
| #23782798 | 3 |
| #23782794 | 3 |
| #23782783 | 3 |
| C3×C43×C32⋊C9 | 3 |
| #10624896 | 43 |