Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
592 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 145 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×Q16×D29 | C2 | semidirect |
| 2. C2×SD16×D29 | C2 | semidirect |
| 4. #124×D29 | C2 | semidirect |
| 5. #14271548 | C2 | semidirect |
| 6. #14271547 | C2 | semidirect |
| 7. #14271546 | C2 | semidirect |
| 8. #14271545 | C2 | semidirect |
| 9. #14271544 | C2 | semidirect |
| 10. C4×C8×D29 | C2 | semidirect |
| 11. C29×#495 | C2 | semidirect |
| 14. C2×Q16×C29 | C22 | semidirect |
| 15. C2×SD16×C29 | C22 | semidirect |
| 17. C29×#124 | C22 | semidirect |
| 18. #11745309 | C22 | semidirect |
| 19. C2×#90785 | C22 | semidirect |
| 20. C2×#90784 | C22 | semidirect |
| 21. #11745298 | C22 | semidirect |
| 22. C2×#90783 | C22 | semidirect |
| 27. C2×Dic116 | C22 | semidirect |
| 29. C2×#90773 | C22 | semidirect |
| 34. #11745237 | C22 | semidirect |
| 36. C4×C8×C29 | C22 | semidirect |
| 37. C8×Dic29 | C22 | semidirect |
| 38. C8×Dic29 | C22 | semidirect |
| 39. C4×#6597 | C22 | semidirect |
| 131. #495 | D29 | direct (N × H) |
| 137. D29 | #495 | direct (N × H) |
| 143. C2×Q16 | C2×D29 | semidirect |
| 148. C2×SD16 | C2×D29 | semidirect |
| 159. #124 | C2×D29 | semidirect |
| 165. C4×C8 | C2×D29 | semidirect |
| 166. C29 | C2×#495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D29 | 2 |
| C2×SD16×D29 | 2 |
| C2×D8×D29 | 2 |
| #124×D29 | 2 |
| #14271548 | 2 |
| #14271547 | 2 |
| #14271546 | 2 |
| #14271545 | 2 |
| #14271544 | 2 |
| C4×C8×D29 | 2 |
| C29×#495 | 2 |
| C2×#495 | 29 |