Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
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×D37 | C2 | semidirect |
| 3. C4⋊Q8×D37 | C2 | semidirect |
| 5. #14557928 | C2 | semidirect |
| 6. #14557927 | C2 | semidirect |
| 7. #14557926 | C2 | semidirect |
| 8. #14557925 | C2 | semidirect |
| 9. #14557924 | C2 | semidirect |
| 10. #97×D37 | C2 | semidirect |
| 11. C37×#497 | C2 | semidirect |
| 15. C2×Dic148 | C22 | semidirect |
| 16. C2×#10596942 | C22 | semidirect |
| 17. C2×#10596942 | C22 | semidirect |
| 24. #11924536 | C22 | semidirect |
| 26. #11924534 | C22 | semidirect |
| 34. #11924447 | C22 | semidirect |
| 35. #11924446 | C22 | semidirect |
| 36. C2×Q16×C37 | C22 | semidirect |
| 38. C4⋊Q8×C37 | C22 | semidirect |
| 40. #97×C37 | C22 | semidirect |
| 131. D37 | #497 | direct (N × H) |
| 141. #497 | D37 | direct (N × H) |
| 143. C37 | C2×#497 | semidirect |
| 151. C2×Q16 | C2×D37 | semidirect |
| 161. C4⋊Q8 | C2×D37 | semidirect |
| 172. #97 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D37 | 2 |
| C2×SD16×D37 | 2 |
| C4⋊Q8×D37 | 2 |
| #124×D37 | 2 |
| #14557928 | 2 |
| #14557927 | 2 |
| #14557926 | 2 |
| #14557925 | 2 |
| #14557924 | 2 |
| #97×D37 | 2 |
| C37×#497 | 2 |
| C2×#497 | 37 |