Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 3. #14271571 | C2 | semidirect |
| 4. #14271570 | C2 | semidirect |
| 5. #14271564 | C2 | semidirect |
| 6. #14271563 | C2 | semidirect |
| 50. M16×C29 | Q8 | semidirect |
| 78. #90777 | Q8 | semidirect |
| 167. C29 | #3166 | semidirect |
| 176. M16 | Dic58 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271716 | 2 |
| C2×#11745252 | 2 |
| #14271571 | 2 |
| #14271570 | 2 |
| #14271564 | 2 |
| #14271563 | 2 |
| #14271206 | 2 |
| #14271205 | 2 |
| #14271203 | 2 |
| M16×Dic29 | 2 |
| C29×#428 | 2 |
| #3166 | 29 |