Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
396 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 87 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. #14271186 | C2 | semidirect |
| 3. C2×#11745181 | C2 | semidirect |
| 4. C2×#11745171 | C2 | semidirect |
| 5. C2×#11745171 | C2 | semidirect |
| 6. M16×Dic29 | C2 | semidirect |
| 7. C2×C29×#100 | C2 | semidirect |
| 48. M16×C29 | D4 | semidirect |
| 57. #90777 | D4 | semidirect |
| 110. Dic29 | #100 | semidirect |
| 116. C2×#100 | D29 | semidirect |
| 142. C29 | #1965 | semidirect |
| 169. M16 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745302 | 2 |
| #14271186 | 2 |
| C2×#11745181 | 2 |
| C2×#11745171 | 2 |
| M16×Dic29 | 2 |
| C2×C29×#100 | 2 |
| #1965 | 29 |