Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
552 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 185 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. #31773791 | C2 | semidirect |
| 3. #31773791 | C2 | semidirect |
| 4. #31773778 | C2 | semidirect |
| 6. C4×Dic271⋊C4 | C2 | semidirect |
| 7. C22⋊C4×Dic271 | C2 | semidirect |
| 8. C22⋊C4×Dic271 | C2 | semidirect |
| 12. #22576141 | C4 | semidirect |
| 36. C22×Dic271 | C2×C4 | semidirect |
| 42. Dic271⋊C4 | C2×C4 | semidirect |
| 46. C22⋊Dic271 | C2×C4 | semidirect |
| 126. C271 | #2374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576141 | 2 |
| #31773791 | 2 |
| #31773778 | 2 |
| #31773777 | 2 |
| C4×Dic271⋊C4 | 2 |
| C22⋊C4×Dic271 | 2 |
| #390×C271 | 2 |
| #2374 | 271 |