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×#11924584 | C2 | semidirect |
| 2. C2×#11924564 | C2 | semidirect |
| 3. C22×#10596941 | C2 | semidirect |
| 4. #14558102 | C2 | semidirect |
| 5. #14557681 | C2 | semidirect |
| 6. #14557673 | C2 | semidirect |
| 7. #14557527 | C2 | semidirect |
| 8. #14557501 | C2 | semidirect |
| 9. C37×#419 | C2 | semidirect |
| 13. C2×#10596966 | C22 | semidirect |
| 18. C2×Q8×D37 | C22 | semidirect |
| 30. #11924459 | C22 | semidirect |
| 31. #11924456 | C22 | semidirect |
| 32. #11924448 | C22 | semidirect |
| 36. #103×C37 | C22 | semidirect |
| 40. C2×Q8×C37 | D4 | semidirect |
| 56. #10596962 | D4 | semidirect |
| 152. #419 | D37 | semidirect |
| 155. C37 | #3010 | semidirect |
| 180. #103 | C2×D37 | semidirect |
| 200. C2×Q8 | D148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924584 | 2 |
| C2×#11924564 | 2 |
| C22×#10596941 | 2 |
| #14558102 | 2 |
| #14557681 | 2 |
| #14557673 | 2 |
| #14557527 | 2 |
| #14557501 | 2 |
| C37×#419 | 2 |
| #3010 | 37 |