Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
564 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 564 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 |
| 3. C4⋊Q8×D29 | C2 | semidirect |
| 5. #14271558 | C2 | semidirect |
| 6. #14271557 | C2 | semidirect |
| 7. #14271556 | C2 | semidirect |
| 8. #14271555 | C2 | semidirect |
| 9. #14271554 | C2 | semidirect |
| 10. #97×D29 | C2 | semidirect |
| 11. C29×#497 | C2 | semidirect |
| 15. C2×Q16×C29 | C22 | semidirect |
| 17. C29×C4⋊Q8 | C22 | semidirect |
| 20. #11745306 | C22 | semidirect |
| 21. C2×#90785 | C22 | semidirect |
| 22. C2×#90785 | C22 | semidirect |
| 28. C2×Dic116 | C22 | semidirect |
| 37. #11745231 | C22 | semidirect |
| 38. C29×#97 | C22 | semidirect |
| 39. #11745163 | C22 | semidirect |
| 40. #11745151 | C22 | semidirect |
| 136. #497 | D29 | direct (N × H) |
| 142. D29 | #497 | direct (N × H) |
| 150. C2×Q16 | C2×D29 | semidirect |
| 160. C4⋊Q8 | C2×D29 | semidirect |
| 171. #97 | C2×D29 | semidirect |
| 172. C29 | C2×#497 | 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 |
| C4⋊Q8×D29 | 2 |
| #124×D29 | 2 |
| #14271558 | 2 |
| #14271557 | 2 |
| #14271556 | 2 |
| #14271555 | 2 |
| #14271554 | 2 |
| #97×D29 | 2 |
| C29×#497 | 2 |
| C2×#497 | 29 |