Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
110 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 23 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 |
|---|---|---|
| 6. #22576160 | C4 | semidirect |
| 8. C4×C271⋊C8 | C4 | semidirect |
| 49. C271 | #1409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774269 | 2 |
| #31773690 | 2 |
| #353×C271 | 2 |
| #1409 | 271 |