Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
326 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 69 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. C2×#11745173 | C2 | semidirect |
| 3. #14271162 | C2 | semidirect |
| 4. C2×#11745171 | C2 | semidirect |
| 5. #14271064 | C2 | semidirect |
| 6. #14270922 | C2 | semidirect |
| 7. C29×#428 | C2 | semidirect |
| 48. M16×C29 | D4 | semidirect |
| 125. #428 | D29 | semidirect |
| 157. C29 | #2037 | semidirect |
| 181. M16 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271732 | 2 |
| C2×#11745173 | 2 |
| #14271162 | 2 |
| C2×#11745171 | 2 |
| #14271064 | 2 |
| #14270922 | 2 |
| C29×#428 | 2 |
| #2037 | 29 |