Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#11745311 | C2 | semidirect |
| 2. C22×#90782 | C2 | semidirect |
| 3. C2×#11745181 | C2 | semidirect |
| 4. C2×#11745171 | C2 | semidirect |
| 5. #14271130 | C2 | semidirect |
| 6. #14270927 | C2 | semidirect |
| 7. C2×C29×AGL(1,ℤ/8) | C2 | semidirect |
| 127. C2×AGL(1,ℤ/8) | D29 | semidirect |
| 161. C29 | #2018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745311 | 2 |
| C22×#90782 | 2 |
| C2×#11745181 | 2 |
| C2×#11745171 | 2 |
| #14271130 | 2 |
| #14270927 | 2 |
| C2×C29×AGL(1,ℤ/8) | 2 |
| #2018 | 29 |