Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
488 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 2. C32⋊C9×C43⋊C3 | C3 | semidirect |
| 3. C32⋊C9×C43⋊C3 | C3 | semidirect |
| 4. #23782697 | C3 | semidirect |
| 5. #23782696 | C3 | semidirect |
| 6. #23782695 | C3 | semidirect |
| 7. C43×#6859 | C3 | semidirect |
| 15. C32⋊(C43⋊C9) | C32 | semidirect |
| 16. C32⋊(C43⋊C9) | C32 | semidirect |
| 20. C43×C32⋊C9 | C32 | semidirect |
| 21. C43×C32⋊C9 | C32 | semidirect |
| 71. #6859 | C43⋊C3 | direct (N × H) |
| 79. C43⋊C3 | #6859 | direct (N × H) |
| 92. C32⋊C9 | C3×C43⋊C3 | semidirect |
| 93. C32⋊C9 | C3×C43⋊C3 | semidirect |
| 94. C43 | C3×#6859 | 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 |
| C32⋊C9×C43⋊C3 | 3 |
| #23782697 | 3 |
| #23782696 | 3 |
| #23782695 | 3 |
| C43×#6859 | 3 |
| C3×#6859 | 43 |