Finite Group DatabasebetaFinite Group DatabasebetaOrder 35008.
298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 103 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×#22576775 | C2 | semidirect |
| 2. C2×D4×D547 | C2 | semidirect |
| 3. #31776026 | C2 | direct (N × H) |
| 4. C2×#22576765 | C2 | semidirect |
| 5. C2×#22576764 | C2 | semidirect |
| 6. C2×#22576761 | C2 | semidirect |
| 7. C2×#22576759 | C2 | semidirect |
| 8. C2×D8×C547 | C2 | semidirect |
| 11. #22576775 | C22 | semidirect |
| 12. C2×Dic1094 | C22 | semidirect |
| 17. D4×D547 | C22 | semidirect |
| 20. #22576765 | C22 | semidirect |
| 21. #22576764 | C22 | semidirect |
| 22. #22576761 | C22 | semidirect |
| 23. #22576759 | C22 | semidirect |
| 24. C2×C547⋊C8 | C22 | semidirect |
| 26. C2×D4×C547 | C22 | semidirect |
| 27. D8×C547 | C22 | semidirect |
| 28. C2×C8×C547 | C22 | semidirect |
| 34. Dic1094 | C23 | semidirect |
| 44. C547⋊C8 | C23 | semidirect |
| 50. D4×C547 | C23 | semidirect |
| 52. C8×C547 | C23 | semidirect |
| 69. C2×C547 | AGL(1,ℤ/8) | semidirect |
| 73. C547 | C2×AGL(1,ℤ/8) | semidirect |
| 81. C2×D8 | D547 | semidirect |
| 93. C2×D4 | C2×D547 | semidirect |
| 99. D8 | C2×D547 | semidirect |
| 102. C2×C8 | C2×D547 | semidirect |
| 118. D4 | C22×D547 | semidirect |
| 126. C8 | C22×D547 | semidirect |
| 145. C2 | #31776026 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576775 | 2 |
| C2×D4×D547 | 2 |
| #31776026 | 2 |
| C2×#22576765 | 2 |
| C2×#22576764 | 2 |
| C2×#22576761 | 2 |
| C2×#22576759 | 2 |
| C2×D8×C547 | 2 |
| C2×AGL(1,ℤ/8) | 547 |