Finite Group DatabasebetaFinite Group DatabasebetaOrder 35008.
262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 262 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. #41×D547 | C2 | semidirect |
| 2. #31776034 | C2 | semidirect |
| 3. #31776031 | C2 | semidirect |
| 4. #31776029 | C2 | semidirect |
| 5. #31776026 | C2 | semidirect |
| 6. #31776024 | C2 | semidirect |
| 7. #31776022 | C2 | semidirect |
| 8. C2×#22576759 | C2 | semidirect |
| 9. #135×C547 | C2 | semidirect |
| 12. #22576776 | C22 | semidirect |
| 15. Q8×D547 | C22 | semidirect |
| 17. D4×D547 | C22 | semidirect |
| 20. Dic2188 | C22 | semidirect |
| 21. #22576766 | C22 | semidirect |
| 22. #22576765 | C22 | semidirect |
| 23. #22576764 | C22 | semidirect |
| 24. #22576763 | C22 | semidirect |
| 25. D4376 | C22 | semidirect |
| 26. #22576761 | C22 | semidirect |
| 27. #22576759 | C22 | semidirect |
| 28. #22576759 | C22 | semidirect |
| 29. C2×C547⋊C8 | C22 | semidirect |
| 30. #41×C547 | C22 | semidirect |
| 31. Q16×C547 | C22 | semidirect |
| 32. SD16×C547 | C22 | semidirect |
| 33. D8×C547 | C22 | semidirect |
| 34. C2×C8×C547 | C22 | semidirect |
| 75. C547 | #575 | semidirect |
| 84. #135 | D547 | semidirect |
| 91. #41 | C2×D547 | semidirect |
| 99. Q16 | C2×D547 | semidirect |
| 103. SD16 | C2×D547 | semidirect |
| 106. D8 | C2×D547 | semidirect |
| 110. C2×C8 | C2×D547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D547 | 2 |
| #31776034 | 2 |
| #31776031 | 2 |
| #31776029 | 2 |
| #31776026 | 2 |
| #31776024 | 2 |
| #31776022 | 2 |
| C2×#22576759 | 2 |
| #135×C547 | 2 |
| #575 | 547 |