Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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×C4⋊Dic271 | C2 | semidirect |
| 3. #31774233 | C2 | semidirect |
| 4. #31774228 | C2 | semidirect |
| 5. #31774216 | C2 | semidirect |
| 6. #31774211 | C2 | semidirect |
| 7. #31773939 | C2 | semidirect |
| 8. #31773899 | C2 | semidirect |
| 9. #407×C271 | C2 | semidirect |
| 27. #22576094 | C22 | semidirect |
| 28. #22576092 | C22 | semidirect |
| 29. #22576085 | C22 | semidirect |
| 30. #22576082 | C22 | semidirect |
| 130. C271 | #3092 | semidirect |
| 140. #407 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774408 | 2 |
| C22×C4⋊Dic271 | 2 |
| #31774233 | 2 |
| #31774228 | 2 |
| #31774216 | 2 |
| #31774211 | 2 |
| #31773939 | 2 |
| #31773899 | 2 |
| #407×C271 | 2 |
| #3092 | 271 |