Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
578 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 97 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. #14271019 | C2 | semidirect |
| 4. #14270929 | C2 | semidirect |
| 10. C29×#120 | C4 | semidirect |
| 25. C24×C29 | C2×C4 | semidirect |
| 38. C22×Dic29 | D4 | semidirect |
| 41. C22⋊C4×C29 | C2×C4 | semidirect |
| 66. C23×C29 | C22⋊C4 | semidirect |
| 79. C2×C4×C29 | C22⋊C4 | semidirect |
| 129. #120 | Dic29 | semidirect |
| 139. C29 | #1889 | semidirect |
| 145. C24 | C2×Dic29 | semidirect |
| 168. C22⋊C4 | C2×Dic29 | semidirect |
| 186. C23 | C22⋊Dic29 | semidirect |
| 204. C2×C4 | C22⋊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 |
| #14271019 | 2 |
| #14270929 | 2 |
| C2×C29×#120 | 2 |
| #1889 | 29 |