Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#22576119 | C2 | semidirect |
| 3. #31774222 | C2 | semidirect |
| 4. #31774216 | C2 | semidirect |
| 5. #31774211 | C2 | semidirect |
| 6. #31773939 | C2 | semidirect |
| 7. #31773903 | C2 | semidirect |
| 8. #407×C271 | C2 | semidirect |
| 18. #22576119 | C22 | semidirect |
| 20. C2×C4⋊Dic271 | C22 | semidirect |
| 21. C2×C4⋊Dic271 | C22 | semidirect |
| 25. #22576094 | C22 | semidirect |
| 26. #22576092 | C22 | semidirect |
| 27. #22576082 | C22 | semidirect |
| 28. #22576082 | C22 | semidirect |
| 31. C22⋊C8×C271 | C22 | semidirect |
| 32. C22⋊C8×C271 | C22 | semidirect |
| 125. C271 | #3094 | semidirect |
| 134. #407 | D271 | semidirect |
| 157. C22⋊C8 | C2×D271 | semidirect |
| 158. C22⋊C8 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576134 | 2 |
| C2×#22576119 | 2 |
| #31774222 | 2 |
| #31774216 | 2 |
| #31774211 | 2 |
| #31773939 | 2 |
| #31773903 | 2 |
| #407×C271 | 2 |
| #3094 | 271 |