Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 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 |
|---|---|---|
| 1. C2×#22576185 | C2 | semidirect |
| 2. C2×#22576185 | C2 | semidirect |
| 3. #31774664 | C2 | semidirect |
| 4. #31774165 | C2 | semidirect |
| 5. #31774162 | C2 | semidirect |
| 6. #31773945 | C2 | semidirect |
| 7. #31773881 | C2 | semidirect |
| 8. C2×#22576076 | C2 | semidirect |
| 9. #575×C271 | C2 | semidirect |
| 16. C2×#16864641 | C22 | semidirect |
| 18. C2×#16864639 | C22 | semidirect |
| 20. #22576167 | C22 | semidirect |
| 25. #22576095 | C22 | semidirect |
| 26. #22576079 | C22 | semidirect |
| 27. #22576077 | C22 | semidirect |
| 28. #22576076 | C22 | semidirect |
| 32. #137×C271 | C22 | semidirect |
| 34. AGL(1,ℤ/8)×C271 | C22 | semidirect |
| 147. C271 | #3068 | semidirect |
| 149. #575 | D271 | semidirect |
| 162. #137 | C2×D271 | semidirect |
| 168. 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×#22576185 | 2 |
| #31774664 | 2 |
| #31774165 | 2 |
| #31774162 | 2 |
| #31773945 | 2 |
| #31773881 | 2 |
| C2×#22576076 | 2 |
| #575×C271 | 2 |
| #3068 | 271 |