Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
246 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 57 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. #31774213 | C2 | semidirect |
| 2. #31773836 | C2 | semidirect |
| 3. #31773631 | C2 | semidirect |
| 4. #31773623 | C2 | semidirect |
| 82. C271 | #1616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774213 | 2 |
| #31773836 | 2 |
| #31773631 | 2 |
| #31773623 | 2 |
| #537×C271 | 2 |
| #1616 | 271 |