Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
174 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 67 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. D8×Dic29 | C2 | semidirect |
| 2. #14270989 | C2 | semidirect |
| 3. #14270964 | C2 | semidirect |
| 4. C16×Dic29 | C2 | semidirect |
| 8. C29×D16 | C4 | semidirect |
| 17. D8×C29 | C2×C4 | semidirect |
| 23. C16×C29 | C2×C4 | semidirect |
| 45. Dic29 | D16 | direct (N × H) |
| 57. D16 | Dic29 | direct (N × H) |
| 63. C29 | C4×D16 | semidirect |
| 67. D8 | C2×Dic29 | semidirect |
| 74. C16 | C2×Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic29 | 2 |
| #14270989 | 2 |
| #14270964 | 2 |
| C16×Dic29 | 2 |
| C2×C29×D16 | 2 |
| C4×D16 | 29 |