Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
266 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 61 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×#11745174 | C2 | semidirect |
| 2. #14271399 | C2 | semidirect |
| 3. #14270964 | C2 | semidirect |
| 4. C22⋊#90768 | C2 | semidirect |
| 5. C22×D8×C29 | C2 | semidirect |
| 12. C2×D232 | C22 | semidirect |
| 15. #11745166 | C22 | semidirect |
| 16. C2×#90768 | C22 | semidirect |
| 27. D8×C29 | D4 | semidirect |
| 61. C22×C29 | D16 | semidirect |
| 70. C22×D8 | D29 | semidirect |
| 92. C29 | #2184 | semidirect |
| 104. D8 | C22⋊D29 | semidirect |
| 139. C22 | #11745174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745174 | 2 |
| #14271399 | 2 |
| #14270964 | 2 |
| C22⋊#90768 | 2 |
| C22×D8×C29 | 2 |
| #2184 | 29 |