Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
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×#11745182 | C2 | semidirect |
| 3. #14270951 | C2 | direct (N × H) |
| 4. C2×C29×#100 | C2 | semidirect |
| 5. C24×D29 | C4 | semidirect |
| 10. C2×C22⋊Dic29 | C4 | semidirect |
| 13. #11745299 | C4 | semidirect |
| 17. C29×#100 | C22 | semidirect |
| 19. #11745182 | C22 | semidirect |
| 27. C23×D29 | C2×C4 | semidirect |
| 46. C22⋊Dic29 | C2×C4 | semidirect |
| 117. C2×#100 | D29 | semidirect |
| 126. C2×C29 | AΣL(1,𝔽16) | semidirect |
| 141. #100 | C2×D29 | semidirect |
| 144. C29 | C2×AΣL(1,𝔽16) | semidirect |
| 247. C2 | #14270951 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745299 | 2 |
| C2×#11745182 | 2 |
| #14270951 | 2 |
| C2×C29×#100 | 2 |
| C2×AΣL(1,𝔽16) | 29 |