Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#22576207 | C2 | semidirect |
| 2. #31774695 | C2 | semidirect |
| 3. #31774468 | C2 | semidirect |
| 4. #31774078 | C2 | semidirect |
| 5. #31774068 | C2 | semidirect |
| 6. #31773914 | C2 | semidirect |
| 7. #31773913 | C2 | semidirect |
| 8. C2×#22576078 | C2 | semidirect |
| 9. #575×C271 | C2 | semidirect |
| 21. #22576191 | C22 | semidirect |
| 23. #22576186 | C22 | semidirect |
| 27. #22576158 | C22 | semidirect |
| 28. #22576147 | C22 | semidirect |
| 32. #22576087 | C22 | semidirect |
| 33. #22576086 | C22 | semidirect |
| 34. #22576078 | C22 | semidirect |
| 38. #137×C271 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C271 | C22 | semidirect |
| 185. C271 | #3020 | semidirect |
| 189. #575 | D271 | semidirect |
| 212. #137 | C2×D271 | semidirect |
| 216. AGL(1,ℤ/8) | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576207 | 2 |
| #31774695 | 2 |
| #31774468 | 2 |
| #31774078 | 2 |
| #31774068 | 2 |
| #31773914 | 2 |
| #31773913 | 2 |
| C2×#22576078 | 2 |
| #575×C271 | 2 |
| #3020 | 271 |