Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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×#11745311 | C2 | semidirect |
| 2. C22×#90782 | C2 | semidirect |
| 3. C2×#11745310 | C2 | semidirect |
| 4. #14271431 | C2 | direct (N × H) |
| 5. C2×#11745170 | C2 | semidirect |
| 6. C2×#11745181 | C2 | semidirect |
| 7. C2×#11745171 | C2 | semidirect |
| 8. C2×C29×AGL(1,ℤ/8) | C2 | semidirect |
| 13. C29×AGL(1,ℤ/8) | C22 | semidirect |
| 18. #11745311 | C22 | semidirect |
| 20. #11745310 | C22 | semidirect |
| 26. C2×#90782 | C22 | semidirect |
| 32. #11745181 | C22 | semidirect |
| 33. #11745171 | C22 | semidirect |
| 34. #11745170 | C22 | semidirect |
| 138. C2×AGL(1,ℤ/8) | D29 | semidirect |
| 149. C2×C29 | #472 | semidirect |
| 158. AGL(1,ℤ/8) | C2×D29 | semidirect |
| 178. C29 | C2×#472 | semidirect |
| 285. C2 | #14271431 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745311 | 2 |
| C22×#90782 | 2 |
| C2×#11745310 | 2 |
| #14271431 | 2 |
| C2×#11745170 | 2 |
| C2×#11745181 | 2 |
| C2×#11745171 | 2 |
| C2×C29×AGL(1,ℤ/8) | 2 |
| C2×#472 | 29 |