Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11924583 | C2 | semidirect |
| 2. C22×#10596940 | C2 | semidirect |
| 3. #14558100 | C2 | semidirect |
| 4. #14557675 | C2 | semidirect |
| 5. #14557670 | C2 | semidirect |
| 6. #14557543 | C2 | semidirect |
| 7. #14557529 | C2 | semidirect |
| 8. #14557501 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C37 | C2 | semidirect |
| 15. C2×#10596964 | C22 | semidirect |
| 18. C2×Q8×D37 | C22 | semidirect |
| 27. #11924461 | C22 | semidirect |
| 28. #11924460 | C22 | semidirect |
| 29. #11924457 | C22 | semidirect |
| 30. #11924448 | C22 | semidirect |
| 39. #41×C37 | D4 | semidirect |
| 70. C2×Dic74 | D4 | semidirect |
| 147. C2×AGL(1,ℤ/8) | D37 | semidirect |
| 155. C37 | #3010 | semidirect |
| 191. #41 | C22⋊D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924583 | 2 |
| C22×#10596940 | 2 |
| #14558100 | 2 |
| #14557675 | 2 |
| #14557670 | 2 |
| #14557543 | 2 |
| #14557529 | 2 |
| #14557501 | 2 |
| C2×AGL(1,ℤ/8)×C37 | 2 |
| #3010 | 37 |