Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 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. #31774380 | C2 | semidirect |
| 3. #31774222 | C2 | semidirect |
| 4. #31774222 | C2 | semidirect |
| 5. #31774216 | C2 | semidirect |
| 6. #31774211 | C2 | semidirect |
| 7. #31773939 | C2 | semidirect |
| 8. #31773935 | C2 | semidirect |
| 9. #31773903 | C2 | semidirect |
| 10. C2×#22576082 | C2 | semidirect |
| 11. #408×C271 | C2 | semidirect |
| 23. #22576119 | C22 | semidirect |
| 25. C2×C4⋊Dic271 | C22 | semidirect |
| 26. #22576094 | C22 | semidirect |
| 27. #22576094 | C22 | semidirect |
| 28. #22576094 | C22 | semidirect |
| 29. #22576092 | C22 | semidirect |
| 30. #22576092 | C22 | semidirect |
| 31. #22576092 | C22 | semidirect |
| 39. C22⋊C8×C271 | C22 | semidirect |
| 40. C22⋊C8×C271 | C22 | semidirect |
| 134. C271 | #3096 | semidirect |
| 146. #408 | D271 | semidirect |
| 174. C22⋊C8 | C2×D271 | semidirect |
| 175. C22⋊C8 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774461 | 2 |
| #31774380 | 2 |
| #31774222 | 2 |
| #31774216 | 2 |
| #31774211 | 2 |
| #31773939 | 2 |
| #31773935 | 2 |
| #31773903 | 2 |
| C2×#22576082 | 2 |
| #408×C271 | 2 |
| #3096 | 271 |