Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 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. C22×C8×D37 | C2 | semidirect |
| 2. C2×#11924512 | C2 | semidirect |
| 4. #14557759 | C2 | direct (N × H) |
| 5. C2×#11924468 | C2 | semidirect |
| 6. C2×#11924460 | C2 | semidirect |
| 7. C2×#11924457 | C2 | semidirect |
| 8. C22×SD16×C37 | C2 | semidirect |
| 13. C2×C8×D37 | C22 | semidirect |
| 15. #11924512 | C22 | semidirect |
| 23. #11924468 | C22 | semidirect |
| 24. #11924460 | C22 | semidirect |
| 25. #11924457 | C22 | semidirect |
| 29. C2×SD16×C37 | C22 | semidirect |
| 53. C2×C8×C37 | D4 | semidirect |
| 72. C22×D37 | SD16 | semidirect |
| 96. C8×C37 | C2×D4 | semidirect |
| 109. C2×D37 | C2×SD16 | semidirect |
| 119. C2×C37 | #465 | semidirect |
| 124. C22×SD16 | D37 | semidirect |
| 132. C37 | C2×#465 | semidirect |
| 138. C2×SD16 | C2×D37 | semidirect |
| 180. C2×C8 | C22⋊D37 | semidirect |
| 221. C8 | C2×C22⋊D37 | semidirect |
| 243. C2 | #14557759 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D37 | 2 |
| C2×#11924512 | 2 |
| C2×#11924507 | 2 |
| #14557759 | 2 |
| C2×#11924468 | 2 |
| C2×#11924460 | 2 |
| C2×#11924457 | 2 |
| C22×SD16×C37 | 2 |
| C2×#465 | 37 |