Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 153 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×#16864654 | C2 | semidirect |
| 2. C2×#22576188 | C2 | semidirect |
| 3. C2×#22576134 | C2 | semidirect |
| 4. #31774044 | C2 | semidirect |
| 5. #31774038 | C2 | semidirect |
| 6. #31774033 | C2 | semidirect |
| 7. #31773899 | C2 | semidirect |
| 8. #407×C271 | C2 | semidirect |
| 13. C2×#16864654 | C22 | semidirect |
| 14. C22×Dic542 | C22 | semidirect |
| 15. C22×D1084 | C22 | semidirect |
| 16. C22×D1084 | C22 | semidirect |
| 21. C2×#16864643 | C22 | semidirect |
| 22. C2×D2168 | C22 | semidirect |
| 26. #22576134 | C22 | semidirect |
| 27. C2×C4⋊Dic271 | C22 | semidirect |
| 29. #22576085 | C22 | semidirect |
| 30. #22576082 | C22 | semidirect |
| 32. C2×M16×C271 | C22 | semidirect |
| 33. C22⋊C8×C271 | C22 | semidirect |
| 34. C22⋊C8×C271 | C22 | semidirect |
| 42. #16864654 | D4 | semidirect |
| 89. Dic542 | C2×D4 | semidirect |
| 94. D1084 | C2×D4 | semidirect |
| 131. C22×C271 | AGL(1,ℤ/8) | semidirect |
| 155. C271 | #3006 | semidirect |
| 164. #407 | D271 | semidirect |
| 180. C2×M16 | C2×D271 | semidirect |
| 189. C22⋊C8 | C2×D271 | semidirect |
| 190. C22⋊C8 | C2×D271 | semidirect |
| 295. C22 | #22576188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864654 | 2 |
| C2×#22576188 | 2 |
| C2×#22576134 | 2 |
| #31774044 | 2 |
| #31774038 | 2 |
| #31774033 | 2 |
| #31773899 | 2 |
| #407×C271 | 2 |
| #3006 | 271 |