Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
312 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 88 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. C3×#16812503 | C3 | semidirect |
| 3. C27⋊C3×C43⋊C3 | C3 | semidirect |
| 4. #23782728 | C3 | semidirect |
| 5. #23782727 | C3 | semidirect |
| 6. #23782726 | C3 | semidirect |
| 7. C43×#6872 | C3 | semidirect |
| 18. #16812505 | C32 | semidirect |
| 23. C3×C43⋊C27 | C32 | semidirect |
| 26. C43×C27⋊C3 | C32 | semidirect |
| 27. C3×C27×C43 | C32 | semidirect |
| 78. #6872 | C43⋊C3 | semidirect |
| 101. C27⋊C3 | C3×C43⋊C3 | semidirect |
| 104. C3×C27 | C3×C43⋊C3 | semidirect |
| 105. C43 | #10624702 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #737×C43⋊C3 | 3 |
| C3×#16812503 | 3 |
| C27⋊C3×C43⋊C3 | 3 |
| #23782728 | 3 |
| #23782727 | 3 |
| #23782726 | 3 |
| C43×#6872 | 3 |
| #10624702 | 43 |