Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
448 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 448 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. C22×Dic116 | C2 | semidirect |
| 3. #14271438 | C2 | direct (N × H) |
| 4. C2×#11745167 | C2 | semidirect |
| 5. C2×#11745172 | C2 | semidirect |
| 23. C2×Dic116 | C22 | semidirect |
| 24. #11745172 | C22 | semidirect |
| 25. #11745167 | C22 | semidirect |
| 108. C2×C29 | #473 | semidirect |
| 129. C29 | C2×#473 | semidirect |
| 205. C2 | #14271438 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745313 | 2 |
| C22×Dic116 | 2 |
| #14271438 | 2 |
| C2×#11745167 | 2 |
| C2×#11745172 | 2 |
| C2×C29×#131 | 2 |
| C2×#473 | 29 |