Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 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. #14271501 | C2 | direct (N × H) |
| 3. C2×#11745155 | C2 | semidirect |
| 4. C2×#11745156 | C2 | semidirect |
| 5. C2×#11745183 | C2 | semidirect |
| 6. C2×#11745183 | C2 | semidirect |
| 24. #11745183 | C22 | semidirect |
| 25. #11745183 | C22 | semidirect |
| 27. #11745156 | C22 | semidirect |
| 28. #11745155 | C22 | semidirect |
| 111. C2×C29 | #485 | semidirect |
| 135. C29 | C2×#485 | semidirect |
| 209. C2 | #14271501 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745288 | 2 |
| #14271501 | 2 |
| C2×#11745155 | 2 |
| C2×#11745156 | 2 |
| C2×#11745183 | 2 |
| C2×C22⋊#6597 | 2 |
| C2×C29×C22⋊Q8 | 2 |
| C2×#485 | 29 |