Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
444 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 444 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. #14271637 | C2 | semidirect |
| 3. #14271168 | C2 | semidirect |
| 4. C2×#11745171 | C2 | semidirect |
| 5. #14270924 | C2 | semidirect |
| 6. #14270922 | C2 | semidirect |
| 7. C29×#418 | C2 | semidirect |
| 14. #11745302 | C4 | semidirect |
| 31. C2×D4×C29 | C2×C4 | semidirect |
| 46. C4⋊C4×C29 | D4 | semidirect |
| 51. C4⋊Dic29 | D4 | semidirect |
| 54. C4×Dic29 | C2×C4 | semidirect |
| 112. #418 | D29 | semidirect |
| 138. C29 | #1887 | semidirect |
| 154. C2×D4 | C4×D29 | semidirect |
| 165. C4⋊C4 | 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 |
| #14271637 | 2 |
| #14271168 | 2 |
| C2×#11745171 | 2 |
| #14270924 | 2 |
| #14270922 | 2 |
| C29×#418 | 2 |
| #1887 | 29 |