Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 1. C22×#16864643 | C2 | semidirect |
| 2. #31774468 | C2 | semidirect |
| 4. #31774143 | C2 | semidirect |
| 5. #31774126 | C2 | semidirect |
| 6. #31773935 | C2 | semidirect |
| 7. #31773907 | C2 | semidirect |
| 8. #31773903 | C2 | semidirect |
| 9. C2×#131×C271 | C2 | semidirect |
| 20. #22576139 | C22 | semidirect |
| 25. #22576094 | C22 | semidirect |
| 26. #22576092 | C22 | semidirect |
| 27. #22576085 | C22 | semidirect |
| 32. C2×M16×C271 | C22 | semidirect |
| 34. C22×C8×C271 | C22 | semidirect |
| 67. C2×C8×C271 | D4 | semidirect |
| 120. C271 | #3057 | semidirect |
| 123. C2×#131 | D271 | semidirect |
| 139. C2×M16 | C2×D271 | semidirect |
| 141. C22×C8 | C2×D271 | semidirect |
| 179. C2×C8 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864643 | 2 |
| #31774468 | 2 |
| #31774461 | 2 |
| #31774143 | 2 |
| #31774126 | 2 |
| #31773935 | 2 |
| #31773907 | 2 |
| #31773903 | 2 |
| C2×#131×C271 | 2 |
| #3057 | 271 |