Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
184 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 49 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. #23782820 | C3 | semidirect |
| 2. #23782812 | C3 | semidirect |
| 4. C43⋊#6862 | C3 | semidirect |
| 5. #23782701 | C3 | semidirect |
| 7. #23782691 | C3 | semidirect |
| 8. #23782691 | C3 | semidirect |
| 86. C43 | #10624676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782820 | 3 |
| #23782812 | 3 |
| #23782800 | 3 |
| C43⋊#6862 | 3 |
| #23782701 | 3 |
| #23782695 | 3 |
| #23782691 | 3 |
| C43×#6857 | 3 |
| #10624676 | 43 |