Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
236 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 236 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. #733×C43⋊C3 | C3 | semidirect |
| 3. C92×C43⋊C3 | C3 | semidirect |
| 4. #23782749 | C3 | semidirect |
| 5. #23782748 | C3 | semidirect |
| 6. #23782747 | C3 | semidirect |
| 7. #23782746 | C3 | semidirect |
| 8. #23782745 | C3 | semidirect |
| 9. C43×#6878 | C3 | semidirect |
| 14. #16812515 | C32 | semidirect |
| 15. #16812515 | C32 | semidirect |
| 21. C9×C43⋊C9 | C32 | semidirect |
| 22. C43×#733 | C32 | semidirect |
| 24. C92×C43 | C32 | semidirect |
| 68. #6878 | C43⋊C3 | direct (N × H) |
| 75. C43⋊C3 | #6878 | direct (N × H) |
| 83. #733 | C3×C43⋊C3 | semidirect |
| 90. C92 | C3×C43⋊C3 | semidirect |
| 91. C43 | C3×#6878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #733×C43⋊C3 | 3 |
| #732×C43⋊C3 | 3 |
| C92×C43⋊C3 | 3 |
| #23782749 | 3 |
| #23782748 | 3 |
| #23782747 | 3 |
| #23782746 | 3 |
| #23782745 | 3 |
| C43×#6878 | 3 |
| C3×#6878 | 43 |