Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 420 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. #31774239 | C2 | semidirect |
| 4. #31774233 | C2 | semidirect |
| 5. #31774228 | C2 | semidirect |
| 6. #31774222 | C2 | semidirect |
| 7. #31774216 | C2 | semidirect |
| 8. #31774211 | C2 | semidirect |
| 9. #31773935 | C2 | semidirect |
| 10. #31773894 | C2 | semidirect |
| 11. C2×C22⋊C8×C271 | C2 | semidirect |
| 30. #22576094 | C22 | semidirect |
| 31. #22576094 | C22 | semidirect |
| 32. #22576092 | C22 | semidirect |
| 33. #22576092 | C22 | semidirect |
| 34. #22576085 | C22 | semidirect |
| 35. #22576085 | C22 | semidirect |
| 36. #22576082 | C22 | semidirect |
| 37. #22576082 | C22 | semidirect |
| 143. C271 | #3091 | semidirect |
| 155. C2×C22⋊C8 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774408 | 2 |
| C2×#22576119 | 2 |
| #31774239 | 2 |
| #31774233 | 2 |
| #31774228 | 2 |
| #31774222 | 2 |
| #31774216 | 2 |
| #31774211 | 2 |
| #31773935 | 2 |
| #31773894 | 2 |
| C2×C22⋊C8×C271 | 2 |
| #3091 | 271 |