Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
108 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 37 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. C29×AGL(1,ℤ/8) | C2 | semidirect |
| 2. #11745311 | C2 | semidirect |
| 3. #11745310 | C2 | semidirect |
| 4. C2×#90782 | C2 | semidirect |
| 5. #11745181 | C2 | semidirect |
| 6. #11745171 | C2 | semidirect |
| 7. #11745170 | C2 | semidirect |
| 55. AGL(1,ℤ/8) | D29 | semidirect |
| 61. C29 | #472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×AGL(1,ℤ/8) | 2 |
| #11745311 | 2 |
| #11745310 | 2 |
| C2×#90782 | 2 |
| #11745181 | 2 |
| #11745171 | 2 |
| #11745170 | 2 |
| #472 | 29 |