Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
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. #16813647 | C2 | semidirect |
| 2. C2×#14268632 | C2 | semidirect |
| 3. #16813629 | C2 | semidirect |
| 4. #16813557 | C2 | semidirect |
| 5. #16813539 | C2 | semidirect |
| 6. #16813538 | C2 | semidirect |
| 7. AGL(1,ℤ/8)×C113 | C2 | semidirect |
| 53. C113 | #472 | semidirect |
| 56. AGL(1,ℤ/8) | D113 | semidirect |