Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
224 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 76 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. #23782856 | C3 | semidirect |
| 3. C3×C27×C43⋊C3 | C3 | semidirect |
| 4. #23782730 | C3 | semidirect |
| 5. #23782729 | C3 | semidirect |
| 6. #23782727 | C3 | semidirect |
| 7. #23782726 | C3 | semidirect |
| 8. #23782717 | C3 | semidirect |
| 9. C43×#6903 | C3 | semidirect |
| 70. #6903 | C43⋊C3 | semidirect |
| 104. C43 | #10624724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782874 | 3 |
| #23782856 | 3 |
| C3×C27×C43⋊C3 | 3 |
| #23782730 | 3 |
| #23782729 | 3 |
| #23782727 | 3 |
| #23782726 | 3 |
| #23782717 | 3 |
| C43×#6903 | 3 |
| #10624724 | 43 |