Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
324 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 1. #14271930 | C2 | semidirect |
| 2. #14271180 | C2 | semidirect |
| 3. #14271168 | C2 | semidirect |
| 4. C2×#11745181 | C2 | semidirect |
| 5. #14270934 | C2 | semidirect |
| 6. #14270921 | C2 | semidirect |
| 12. C2×SD16×C29 | C4 | semidirect |
| 13. C2×D8×C29 | C4 | semidirect |
| 124. C2×SD16 | Dic29 | semidirect |
| 125. C2×D8 | Dic29 | semidirect |
| 137. C29 | #1903 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271930 | 2 |
| #14271180 | 2 |
| #14271168 | 2 |
| C2×#11745181 | 2 |
| #14270934 | 2 |
| #14270921 | 2 |
| C2×C29×AGL(1,ℤ/8) | 2 |
| #1903 | 29 |