Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
174 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 79 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. C22×#90768 | C2 | semidirect |
| 2. C2×C16×D29 | C2 | semidirect |
| 4. #14270981 | C2 | semidirect |
| 5. #14270942 | C2 | semidirect |
| 6. C16×Dic29 | C2 | semidirect |
| 7. C29×C22⋊C16 | C2 | semidirect |
| 39. #90768 | D4 | semidirect |
| 46. C22⋊D29 | C16 | semidirect |
| 60. C22×C29 | C2×C16 | semidirect |
| 64. C2×D29 | C2×C16 | semidirect |
| 70. Dic29 | C2×C16 | semidirect |
| 76. C22⋊C16 | D29 | semidirect |
| 96. C29 | D4×C16 | semidirect |
| 138. C22 | C16×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90768 | 2 |
| C2×C16×D29 | 2 |
| C8×C22⋊D29 | 2 |
| #14270981 | 2 |
| #14270942 | 2 |
| C16×Dic29 | 2 |
| C29×C22⋊C16 | 2 |
| D4×C16 | 29 |