Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
224 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 224 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 |
|---|---|---|
| 2. #23782858 | C3 | semidirect |
| 3. C32×C43⋊C27 | C3 | semidirect |
| 4. #23782729 | C3 | semidirect |
| 5. #23782726 | C3 | semidirect |
| 6. #23782718 | C3 | semidirect |
| 7. C43×#6869 | C3 | semidirect |
| 61. #6869 | C43⋊C3 | semidirect |
| 83. C43 | #10624724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782877 | 3 |
| #23782858 | 3 |
| C32×C43⋊C27 | 3 |
| #23782729 | 3 |
| #23782726 | 3 |
| #23782718 | 3 |
| C43×#6869 | 3 |
| #10624724 | 43 |