Finite Group DatabasebetaFinite Group DatabasebetaOrder 31168.
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. #29510240 | C2 | semidirect |
| 2. C2×#21441246 | C2 | semidirect |
| 3. #29510222 | C2 | semidirect |
| 4. #29510150 | C2 | semidirect |
| 5. #29510132 | C2 | semidirect |
| 6. #29510131 | C2 | semidirect |
| 7. AGL(1,ℤ/8)×C487 | C2 | semidirect |
| 53. C487 | #472 | semidirect |
| 56. AGL(1,ℤ/8) | D487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29510240 | 2 |
| C2×#21441246 | 2 |
| #29510222 | 2 |
| #29510150 | 2 |
| #29510132 | 2 |
| #29510131 | 2 |
| AGL(1,ℤ/8)×C487 | 2 |
| #472 | 487 |