Finite Group DatabasebetaFinite Group DatabasebetaOrder 11072.
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. #19149704 | C2 | semidirect |
| 2. C2×#14583811 | C2 | semidirect |
| 3. #19149686 | C2 | semidirect |
| 4. #19149614 | C2 | semidirect |
| 5. #19149596 | C2 | semidirect |
| 6. #19149595 | C2 | semidirect |
| 7. AGL(1,ℤ/8)×C173 | C2 | semidirect |
| 53. C173 | #472 | semidirect |
| 56. AGL(1,ℤ/8) | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19149704 | 2 |
| C2×#14583811 | 2 |
| #19149686 | 2 |
| #19149614 | 2 |
| #19149596 | 2 |
| #19149595 | 2 |
| AGL(1,ℤ/8)×C173 | 2 |
| #472 | 173 |