Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
380 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 93 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. #14271638 | C2 | semidirect |
| 2. C2×#11745182 | C2 | semidirect |
| 3. C2×#11745182 | C2 | semidirect |
| 4. #14270929 | C2 | semidirect |
| 9. C29×#123 | C4 | semidirect |
| 12. C29×#120 | C4 | semidirect |
| 21. C24×C29 | C2×C4 | semidirect |
| 34. C22×C4×C29 | C2×C4 | semidirect |
| 43. C22⋊C4×C29 | C2×C4 | semidirect |
| 48. C22⋊Dic29 | D4 | semidirect |
| 121. #123 | Dic29 | semidirect |
| 124. #120 | Dic29 | semidirect |
| 133. C29 | #1913 | semidirect |
| 134. C24 | C2×Dic29 | semidirect |
| 150. C22×C4 | C2×Dic29 | semidirect |
| 162. C22⋊C4 | C2×Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271638 | 2 |
| C2×#11745182 | 2 |
| #14270929 | 2 |
| C29×#534 | 2 |
| #1913 | 29 |