Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 752 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 |
|---|---|---|
| 2. C2×#22576191 | C2 | semidirect |
| 3. #31774471 | C2 | semidirect |
| 4. #31774056 | C2 | semidirect |
| 5. #31774046 | C2 | semidirect |
| 6. #31773902 | C2 | semidirect |
| 7. #31773894 | C2 | semidirect |
| 8. #31773863 | C2 | semidirect |
| 9. C22×SD16×C271 | C2 | semidirect |
| 20. C2×#16864644 | C22 | semidirect |
| 21. C2×#16864641 | C22 | semidirect |
| 22. C2×#16864638 | C22 | semidirect |
| 26. #22576136 | C22 | semidirect |
| 27. #22576119 | C22 | semidirect |
| 28. #22576085 | C22 | semidirect |
| 29. #22576082 | C22 | semidirect |
| 30. #22576081 | C22 | semidirect |
| 31. (C2×D271)⋊C8 | C22 | semidirect |
| 32. C22×Q8×C271 | C22 | semidirect |
| 35. C2×SD16×C271 | C22 | semidirect |
| 36. C22×C8×C271 | C22 | semidirect |
| 146. C271 | #3009 | semidirect |
| 150. C22×SD16 | D271 | semidirect |
| 163. C22×Q8 | C2×D271 | semidirect |
| 172. C2×SD16 | C2×D271 | semidirect |
| 174. 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×#22576205 | 2 |
| C2×#22576191 | 2 |
| #31774471 | 2 |
| #31774056 | 2 |
| #31774046 | 2 |
| #31773902 | 2 |
| #31773894 | 2 |
| #31773863 | 2 |
| C22×SD16×C271 | 2 |
| #3009 | 271 |