Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
468 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 149 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. #14271487 | C2 | direct (N × H) |
| 3. C2×#11745155 | C2 | semidirect |
| 4. C2×#11745156 | C2 | semidirect |
| 5. C2×#11745157 | C2 | semidirect |
| 6. C2×#11745157 | C2 | semidirect |
| 7. C2×C22⋊#6597 | C2 | semidirect |
| 8. C2×C29×#117 | C2 | semidirect |
| 13. C29×#117 | C22 | semidirect |
| 24. C22⋊#6597 | C22 | semidirect |
| 25. #11745157 | C22 | semidirect |
| 26. #11745157 | C22 | semidirect |
| 27. #11745156 | C22 | semidirect |
| 28. #11745155 | C22 | semidirect |
| 110. C2×#117 | D29 | semidirect |
| 118. C2×C29 | #482 | semidirect |
| 131. #117 | C2×D29 | semidirect |
| 143. C29 | C2×#482 | semidirect |
| 225. C2 | #14271487 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745292 | 2 |
| #14271487 | 2 |
| C2×#11745155 | 2 |
| C2×#11745156 | 2 |
| C2×#11745157 | 2 |
| C2×C22⋊#6597 | 2 |
| C2×C29×#117 | 2 |
| C2×#482 | 29 |