Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
380 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 157 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. #14271569 | C2 | semidirect |
| 3. #14271566 | C2 | semidirect |
| 4. #14271559 | C2 | semidirect |
| 54. #90777 | Q8 | semidirect |
| 74. #6597 | C2×Q8 | semidirect |
| 121. C29 | #3165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271720 | 2 |
| #14271569 | 2 |
| #14271566 | 2 |
| #14271559 | 2 |
| #14271203 | 2 |
| C4×#90777 | 2 |
| C2×C29×C4⋊Q8 | 2 |
| #3165 | 29 |