Finite Group DatabasebetaFinite Group DatabasebetaOrder 35008.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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. #31776047 | C2 | semidirect |
| 2. #31776028 | C2 | semidirect |
| 3. #31776026 | C2 | semidirect |
| 4. #31776024 | C2 | semidirect |
| 5. #31776021 | C2 | semidirect |
| 6. D8×D547 | C2 | semidirect |
| 7. #31776008 | C2 | semidirect |
| 8. C2×D8×C547 | C2 | semidirect |
| 10. #22576776 | C22 | semidirect |
| 12. #22576775 | C22 | semidirect |
| 15. D4×D547 | C22 | semidirect |
| 16. Dic2188 | C22 | semidirect |
| 17. #22576765 | C22 | semidirect |
| 18. #22576764 | C22 | semidirect |
| 19. D4376 | C22 | semidirect |
| 20. #22576761 | C22 | semidirect |
| 21. #22576760 | C22 | semidirect |
| 22. #22576759 | C22 | semidirect |
| 23. C8×D547 | C22 | semidirect |
| 24. C2×D4×C547 | C22 | semidirect |
| 25. D8×C547 | C22 | semidirect |
| 26. D8×C547 | C22 | semidirect |
| 27. C2×C8×C547 | C22 | semidirect |
| 62. C547 | #576 | semidirect |
| 70. C2×D8 | D547 | semidirect |
| 79. C2×D4 | C2×D547 | semidirect |
| 85. D8 | C2×D547 | semidirect |
| 86. D8 | C2×D547 | semidirect |
| 90. C2×C8 | C2×D547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31776047 | 2 |
| #31776028 | 2 |
| #31776026 | 2 |
| #31776024 | 2 |
| #31776021 | 2 |
| D8×D547 | 2 |
| #31776008 | 2 |
| C2×D8×C547 | 2 |
| #576 | 547 |