Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
756 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 249 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. #14271930 | C2 | semidirect |
| 3. #14271145 | C2 | semidirect |
| 4. C2×#11745171 | C2 | semidirect |
| 5. C29×#568 | C2 | semidirect |
| 14. C2×M16×C29 | C22 | semidirect |
| 16. C2×#90777 | C22 | semidirect |
| 17. #11745172 | C22 | semidirect |
| 18. #11745171 | C22 | semidirect |
| 75. #568 | D29 | semidirect |
| 92. C2×M16 | C2×D29 | semidirect |
| 95. C29 | #2888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745364 | 2 |
| #14271930 | 2 |
| #14271145 | 2 |
| C2×#11745171 | 2 |
| C29×#568 | 2 |
| #2888 | 29 |