Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
224 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 224 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 |
| 2. #732×C43⋊C3 | C3 | semidirect |
| 3. C9⋊C9×C43⋊C3 | C3 | semidirect |
| 4. #23782759 | C3 | semidirect |
| 5. #23782758 | C3 | semidirect |
| 6. #23782757 | C3 | semidirect |
| 7. #23782756 | C3 | semidirect |
| 8. #23782755 | C3 | semidirect |
| 9. C43×#6881 | C3 | semidirect |
| 14. #16812515 | C32 | semidirect |
| 16. #16812513 | C32 | semidirect |
| 17. #16812513 | C32 | semidirect |
| 19. #16812500 | C32 | semidirect |
| 20. #16812499 | C32 | semidirect |
| 22. C43×#733 | C32 | semidirect |
| 23. C43×#732 | C32 | semidirect |
| 24. C43×C9⋊C9 | C32 | semidirect |
| 71. #6881 | C43⋊C3 | direct (N × H) |
| 79. C43⋊C3 | #6881 | direct (N × H) |
| 86. #733 | C3×C43⋊C3 | semidirect |
| 90. #732 | C3×C43⋊C3 | semidirect |
| 94. C9⋊C9 | C3×C43⋊C3 | semidirect |
| 95. C43 | C3×#6881 | 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 |
| C9⋊C9×C43⋊C3 | 3 |
| #23782759 | 3 |
| #23782758 | 3 |
| #23782757 | 3 |
| #23782756 | 3 |
| #23782755 | 3 |
| C43×#6881 | 3 |
| C3×#6881 | 43 |