Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
784 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#16864639 | C2 | semidirect |
| 3. #31774461 | C2 | semidirect |
| 4. #31774042 | C2 | semidirect |
| 5. #31774031 | C2 | semidirect |
| 6. #31773902 | C2 | semidirect |
| 7. #31773893 | C2 | semidirect |
| 8. #31773864 | C2 | semidirect |
| 9. C2×H(5,𝔽2)×C271 | C2 | semidirect |
| 10. C22×D1084 | C22 | semidirect |
| 12. C2×#16864641 | C22 | semidirect |
| 14. C2×#16864639 | C22 | semidirect |
| 15. C2×#16864639 | C22 | semidirect |
| 16. C2×#16864638 | C22 | semidirect |
| 17. C22×C271⋊C8 | C22 | semidirect |
| 20. #22576134 | C22 | semidirect |
| 22. #22576119 | C22 | semidirect |
| 23. #22576084 | C22 | semidirect |
| 24. #22576081 | C22 | semidirect |
| 25. #22576081 | C22 | semidirect |
| 26. C22⋊(C271⋊C8) | C22 | semidirect |
| 32. C2×#41×C271 | C22 | semidirect |
| 36. C22×D4×C271 | C22 | semidirect |
| 62. #41×C271 | D4 | semidirect |
| 76. C2×D4×C271 | D4 | semidirect |
| 151. C271 | #3008 | semidirect |
| 153. C2×H(5,𝔽2) | D271 | semidirect |
| 167. C2×#41 | C2×D271 | semidirect |
| 172. C22×D4 | C2×D271 | semidirect |
| 198. #41 | C22⋊D271 | semidirect |
| 217. C2×D4 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576185 | 2 |
| C22×#16864639 | 2 |
| #31774461 | 2 |
| #31774042 | 2 |
| #31774031 | 2 |
| #31773902 | 2 |
| #31773893 | 2 |
| #31773864 | 2 |
| C2×H(5,𝔽2)×C271 | 2 |
| #3008 | 271 |