Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
186 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 49 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×D464 | C2 | semidirect |
| 2. C2×#11745174 | C2 | semidirect |
| 3. #14271538 | C2 | semidirect |
| 4. #14271245 | C2 | semidirect |
| 5. #14270981 | C2 | semidirect |
| 6. #14270963 | C2 | semidirect |
| 7. C29×#357 | C2 | semidirect |
| 38. D232 | D4 | semidirect |
| 75. Dic29 | D16 | semidirect |
| 82. #357 | D29 | semidirect |
| 102. C29 | #2206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D464 | 2 |
| C2×#11745174 | 2 |
| #14271538 | 2 |
| #14271245 | 2 |
| #14270981 | 2 |
| #14270963 | 2 |
| C29×#357 | 2 |
| #2206 | 29 |