Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
1112 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×C22⋊Dic271 | C2 | semidirect |
| 3. C2×#22576074 | C2 | direct (N × H) |
| 4. C22×C22⋊C4×C271 | C2 | semidirect |
| 5. C24×D271 | C4 | semidirect |
| 10. C22×C22⋊D271 | C4 | semidirect |
| 13. C23×Dic271 | C4 | semidirect |
| 15. C2×C22⋊Dic271 | C22 | semidirect |
| 16. #22576074 | C22 | direct (N × H) |
| 20. C2×C22⋊C4×C271 | C22 | semidirect |
| 24. C23×D271 | C2×C4 | semidirect |
| 32. C2×C22⋊D271 | C2×C4 | semidirect |
| 38. C22×Dic271 | C2×C4 | semidirect |
| 40. C22⋊Dic271 | C23 | semidirect |
| 52. C22⋊C4×C271 | C23 | semidirect |
| 58. C22×D271 | C22×C4 | semidirect |
| 67. C2×Dic271 | C22×C4 | semidirect |
| 100. C22×C271 | #99 | semidirect |
| 121. C2×C271 | C2×#99 | semidirect |
| 124. C271 | C22×#99 | semidirect |
| 128. C22×C22⋊C4 | D271 | semidirect |
| 144. C2×C22⋊C4 | C2×D271 | semidirect |
| 177. C22⋊C4 | C22×D271 | semidirect |
| 229. C22 | #22576074 | direct (N × H) |
| 247. C2 | C2×#22576074 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D271 | 2 |
| C22×C22⋊Dic271 | 2 |
| C2×#22576074 | 2 |
| C22×C22⋊C4×C271 | 2 |
| C22×#99 | 271 |