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. #31776048 | C2 | semidirect |
| 2. #31776029 | C2 | semidirect |
| 3. #31776027 | C2 | semidirect |
| 4. #31776025 | C2 | semidirect |
| 5. C2×D4376 | C2 | semidirect |
| 6. D8×D547 | C2 | semidirect |
| 7. #31776008 | C2 | semidirect |
| 8. #135×C547 | C2 | semidirect |
| 9. #22576777 | C22 | semidirect |
| 13. C2×D2188 | C22 | semidirect |
| 15. D4×D547 | C22 | semidirect |
| 16. #22576763 | C22 | semidirect |
| 17. D4376 | C22 | semidirect |
| 18. D4376 | C22 | semidirect |
| 19. #22576761 | C22 | semidirect |
| 20. #22576760 | C22 | semidirect |
| 21. #22576759 | C22 | semidirect |
| 22. C8×D547 | C22 | semidirect |
| 23. #41×C547 | C22 | semidirect |
| 24. Q16×C547 | C22 | semidirect |
| 25. SD16×C547 | C22 | semidirect |
| 26. D8×C547 | C22 | semidirect |
| 27. C2×C8×C547 | C22 | semidirect |
| 62. C547 | #576 | semidirect |
| 68. #135 | D547 | semidirect |
| 75. #41 | C2×D547 | semidirect |
| 80. Q16 | C2×D547 | semidirect |
| 82. SD16 | 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 |
|---|---|
| #31776048 | 2 |
| #31776029 | 2 |
| #31776027 | 2 |
| #31776025 | 2 |
| C2×D4376 | 2 |
| D8×D547 | 2 |
| #31776008 | 2 |
| #135×C547 | 2 |
| #576 | 547 |