Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
370 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 83 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. #14271644 | C2 | semidirect |
| 3. C2×#11745153 | C2 | semidirect |
| 4. #14271168 | C2 | semidirect |
| 5. #14270932 | C2 | semidirect |
| 6. #14270923 | C2 | semidirect |
| 7. C29×#390 | C2 | semidirect |
| 15. #11745294 | C4 | semidirect |
| 34. C2×D4×C29 | C2×C4 | semidirect |
| 64. #90777 | C2×C4 | semidirect |
| 95. D116 | C22⋊C4 | semidirect |
| 100. Dic58 | C22⋊C4 | semidirect |
| 130. #390 | D29 | semidirect |
| 160. C29 | #1883 | semidirect |
| 174. C2×D4 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745294 | 2 |
| #14271644 | 2 |
| C2×#11745153 | 2 |
| #14271168 | 2 |
| #14270932 | 2 |
| #14270923 | 2 |
| C29×#390 | 2 |
| #1883 | 29 |