Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
280 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 1. C2×#11745181 | C2 | semidirect |
| 2. C2×#11745182 | C2 | semidirect |
| 3. #14270953 | C2 | semidirect |
| 4. #14270950 | C2 | semidirect |
| 6. C22×D4×C29 | C4 | semidirect |
| 9. C29×#123 | C4 | semidirect |
| 14. C29×#120 | C4 | semidirect |
| 16. C2×C22⋊C4×C29 | C4 | semidirect |
| 24. C24×C29 | C2×C4 | semidirect |
| 39. C22×C4×C29 | C2×C4 | semidirect |
| 49. C22⋊C4×C29 | C2×C4 | semidirect |
| 50. C22⋊C4×C29 | C2×C4 | semidirect |
| 132. C22×D4 | Dic29 | semidirect |
| 136. #123 | Dic29 | semidirect |
| 141. #120 | Dic29 | semidirect |
| 144. C2×C22⋊C4 | Dic29 | semidirect |
| 149. C29 | #2121 | semidirect |
| 151. C24 | C2×Dic29 | semidirect |
| 167. C22×C4 | C2×Dic29 | semidirect |
| 181. C22⋊C4 | C2×Dic29 | semidirect |
| 182. C22⋊C4 | C2×Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745181 | 2 |
| C2×#11745182 | 2 |
| #14270953 | 2 |
| #14270950 | 2 |
| C29×#534 | 2 |
| #2121 | 29 |