Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
438 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 77 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×#11745181 | C2 | semidirect |
| 2. C2×#11745182 | C2 | semidirect |
| 3. #14270950 | C2 | direct (N × H) |
| 5. C25×C29 | C4 | semidirect |
| 10. C29×#120 | C4 | semidirect |
| 13. C2×C22⋊C4×C29 | C4 | semidirect |
| 17. #11745182 | C22 | semidirect |
| 19. #11745181 | C22 | semidirect |
| 26. C24×C29 | C2×C4 | semidirect |
| 43. C22⋊C4×C29 | C2×C4 | semidirect |
| 127. C2×C29 | AΣL(1,𝔽16) | semidirect |
| 129. C25 | Dic29 | semidirect |
| 135. #120 | Dic29 | semidirect |
| 139. C2×C22⋊C4 | Dic29 | semidirect |
| 144. C29 | C2×AΣL(1,𝔽16) | semidirect |
| 151. C24 | C2×Dic29 | semidirect |
| 173. C22⋊C4 | C2×Dic29 | semidirect |
| 247. C2 | #14270950 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745181 | 2 |
| C2×#11745182 | 2 |
| #14270950 | 2 |
| C2×C29×#120 | 2 |
| C2×AΣL(1,𝔽16) | 29 |