Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1166 conjugacy classes of subgroups; only the 310 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 310 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. #23782808 | C3 | semidirect |
| 3. #23782803 | C3 | semidirect |
| 4. #23782802 | C3 | semidirect |
| 5. #23782798 | C3 | semidirect |
| 7. C9×C32⋊(C43⋊C3) | C3 | semidirect |
| 8. C33×C9×C43 | C3 | semidirect |
| 11. C3×#11923957 | C32 | semidirect |
| 12. C3×#11923956 | C32 | semidirect |
| 15. C3×C9×C43⋊C3 | C32 | semidirect |
| 17. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 41. C3×C9×C43 | H(3,𝔽3) | semidirect |
| 52. C32×C43 | #737 | semidirect |
| 62. C33×C9 | C43⋊C3 | semidirect |
| 90. C43 | #10624869 | semidirect |
| 107. C3×C9 | C32⋊(C43⋊C3) | semidirect |
| 119. 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 |
| #23782808 | 3 |
| #23782803 | 3 |
| #23782802 | 3 |
| #23782798 | 3 |
| #23782794 | 3 |
| C9×C32⋊(C43⋊C3) | 3 |
| C33×C9×C43 | 3 |
| #10624869 | 43 |