Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
438 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 69 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. C2×#11924451 | C2 | semidirect |
| 3. #14557321 | C2 | direct (N × H) |
| 4. C2×#100×C37 | C2 | semidirect |
| 5. C24×D37 | C4 | semidirect |
| 9. #11924504 | C4 | semidirect |
| 12. C2×C22⋊Dic37 | C4 | semidirect |
| 15. #11924451 | C22 | semidirect |
| 19. #100×C37 | C22 | semidirect |
| 27. C23×D37 | C2×C4 | semidirect |
| 46. C22⋊Dic37 | C2×C4 | semidirect |
| 122. C2×C37 | AΣL(1,𝔽16) | semidirect |
| 126. C2×#100 | D37 | semidirect |
| 129. C37 | C2×AΣL(1,𝔽16) | semidirect |
| 142. #100 | C2×D37 | semidirect |
| 247. C2 | #14557321 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924504 | 2 |
| C2×#11924451 | 2 |
| #14557321 | 2 |
| C2×#100×C37 | 2 |
| C2×AΣL(1,𝔽16) | 37 |