Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
186 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 51 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. #14271538 | C2 | semidirect |
| 3. D8×Dic29 | C2 | semidirect |
| 4. #14270981 | C2 | semidirect |
| 5. #14270965 | C2 | semidirect |
| 6. #14270964 | C2 | semidirect |
| 7. C2×C29×D16 | C2 | semidirect |
| 30. D8×C29 | D4 | semidirect |
| 75. Dic29 | D16 | semidirect |
| 77. C2×D16 | D29 | semidirect |
| 102. C29 | #2206 | semidirect |
| 115. D8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745174 | 2 |
| #14271538 | 2 |
| D8×Dic29 | 2 |
| #14270981 | 2 |
| #14270965 | 2 |
| #14270964 | 2 |
| C2×C29×D16 | 2 |
| #2206 | 29 |