Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
656 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 165 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×SD16×D37 | C2 | semidirect |
| 2. C4⋊Q8×D37 | C2 | semidirect |
| 4. #14557907 | C2 | semidirect |
| 5. #14557906 | C2 | semidirect |
| 6. #14557905 | C2 | semidirect |
| 7. #14557904 | C2 | semidirect |
| 8. C4×C8×D37 | C2 | semidirect |
| 9. C37×#492 | C2 | semidirect |
| 13. C2×#10596930 | C22 | semidirect |
| 14. C2×#10596940 | C22 | semidirect |
| 15. C2×#10596941 | C22 | semidirect |
| 18. #11924536 | C22 | semidirect |
| 20. #11924534 | C22 | semidirect |
| 26. C4×#64436 | C22 | semidirect |
| 27. C8×Dic37 | C22 | semidirect |
| 28. C2×SD16×C37 | C22 | semidirect |
| 29. C4⋊Q8×C37 | C22 | semidirect |
| 31. C4×C8×C37 | C22 | semidirect |
| 60. C8×D37 | D4 | semidirect |
| 80. C4×D37 | SD16 | semidirect |
| 84. C8×C37 | C2×D4 | semidirect |
| 85. #64436 | C2×D4 | semidirect |
| 95. C4×C37 | C2×SD16 | semidirect |
| 99. Dic37 | C2×SD16 | semidirect |
| 105. D37 | #492 | direct (N × H) |
| 113. #492 | D37 | direct (N × H) |
| 115. C37 | C2×#492 | semidirect |
| 123. C2×SD16 | C2×D37 | semidirect |
| 128. C4⋊Q8 | C2×D37 | semidirect |
| 137. C4×C8 | C2×D37 | semidirect |
| 191. C8 | D4×D37 | semidirect |
| 204. C4 | SD16×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×SD16×D37 | 2 |
| C4⋊Q8×D37 | 2 |
| #127×D37 | 2 |
| #14557907 | 2 |
| #14557906 | 2 |
| #14557905 | 2 |
| #14557904 | 2 |
| C4×C8×D37 | 2 |
| C37×#492 | 2 |
| C2×#492 | 37 |