Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 2. #14557881 | C2 | semidirect |
| 3. #14557851 | C2 | semidirect |
| 4. #14557820 | C2 | semidirect |
| 5. #14557764 | C2 | semidirect |
| 6. #14557733 | C2 | semidirect |
| 7. #14557683 | C2 | semidirect |
| 8. C4×#10596941 | C2 | semidirect |
| 9. D4×#64436 | C2 | semidirect |
| 10. C2×#11924456 | C2 | semidirect |
| 11. C37×#554 | C2 | semidirect |
| 15. C2×#10596941 | C22 | semidirect |
| 16. C22×#64436 | C22 | semidirect |
| 22. #11924467 | C22 | semidirect |
| 23. #11924467 | C22 | semidirect |
| 24. C4⋊#64436 | C22 | semidirect |
| 25. #11924460 | C22 | semidirect |
| 28. #11924456 | C22 | semidirect |
| 29. #11924456 | C22 | semidirect |
| 30. #11924456 | C22 | semidirect |
| 31. C22⋊#64436 | C22 | semidirect |
| 32. C4×#64436 | C22 | semidirect |
| 33. C4⋊Q8×C37 | C22 | semidirect |
| 36. C22⋊Q8×C37 | C22 | semidirect |
| 37. C4×Q8×C37 | C22 | semidirect |
| 40. C2×C4⋊C4×C37 | C22 | semidirect |
| 86. D4×C37 | SD16 | semidirect |
| 137. #554 | D37 | semidirect |
| 148. C37 | #3295 | semidirect |
| 154. C4⋊Q8 | C2×D37 | semidirect |
| 158. C22⋊Q8 | C2×D37 | semidirect |
| 162. C4×Q8 | C2×D37 | semidirect |
| 166. C2×C4⋊C4 | C2×D37 | semidirect |
| 231. D4 | #10596941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D148 | 2 |
| #14557881 | 2 |
| #14557851 | 2 |
| #14557820 | 2 |
| #14557764 | 2 |
| #14557733 | 2 |
| #14557683 | 2 |
| C4×#10596941 | 2 |
| D4×#64436 | 2 |
| C2×#11924456 | 2 |
| C37×#554 | 2 |
| #3295 | 37 |