Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
704 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 73 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. C32×#11923958 | C3 | semidirect |
| 2. C32×C32⋊(C43⋊C3) | C3 | semidirect |
| 3. C3×#16812508 | C3 | semidirect |
| 4. #23782794 | C3 | semidirect |
| 5. C43×#6891 | C3 | semidirect |
| 29. #11923958 | H(3,𝔽3) | semidirect |
| 55. C32×C43 | AΣL(1,𝔽27) | semidirect |
| 70. #6891 | C43⋊C3 | semidirect |
| 96. C43 | #10624743 | semidirect |
| 136. C32 | #16812508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11923958 | 3 |
| C32×C32⋊(C43⋊C3) | 3 |
| C3×#16812508 | 3 |
| #23782794 | 3 |
| C43×#6891 | 3 |
| #10624743 | 43 |