Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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. #14271363 | C2 | semidirect |
| 3. Q8×#6597 | C2 | semidirect |
| 4. #14270915 | C2 | semidirect |
| 5. #14270907 | C2 | semidirect |
| 6. #14270906 | C2 | semidirect |
| 7. C29×#460 | C2 | semidirect |
| 46. Q8×C29 | D8 | semidirect |
| 66. #6597 | SD16 | semidirect |
| 84. #460 | D29 | semidirect |
| 109. C29 | #1668 | semidirect |
| 133. Q8 | #90782 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271539 | 2 |
| #14271363 | 2 |
| Q8×#6597 | 2 |
| #14270915 | 2 |
| #14270907 | 2 |
| #14270906 | 2 |
| C29×#460 | 2 |
| #1668 | 29 |