Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
174 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 2. D8×Dic29 | C2 | semidirect |
| 3. #14271245 | C2 | semidirect |
| 4. #14270988 | C2 | semidirect |
| 5. #14270965 | C2 | semidirect |
| 6. C16×Dic29 | C2 | semidirect |
| 7. C29×#357 | C2 | semidirect |
| 15. #11745174 | C4 | semidirect |
| 25. D8×C29 | C2×C4 | semidirect |
| 34. D232 | C2×C4 | semidirect |
| 36. #90768 | C2×C4 | semidirect |
| 66. Dic29 | D16 | semidirect |
| 72. #357 | D29 | semidirect |
| 91. C29 | C4×D16 | semidirect |
| 99. D8 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745174 | 2 |
| D8×Dic29 | 2 |
| #14271245 | 2 |
| #14270988 | 2 |
| #14270965 | 2 |
| C16×Dic29 | 2 |
| C29×#357 | 2 |
| C4×D16 | 29 |