Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
428 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 428 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 |
|---|---|---|
| 4. #23782724 | C3 | semidirect |
| 97. C43 | #10624812 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782798 | 3 |
| #23782724 | 3 |
| C33×C9×C43 | 3 |
| #10624812 | 43 |