Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
340 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 3. #14526960 | C2 | direct (N × H) |
| 5. C2×#10587556 | C4 | semidirect |
| 8. #11763163 | C4 | semidirect |
| 13. C2×C4×#3622 | C4 | semidirect |
| 36. #10587556 | C2×C4 | semidirect |
| 46. C4×#3622 | C2×C4 | semidirect |
| 153. C2×C17 | #1414 | semidirect |
| 182. C17 | C2×#1414 | semidirect |
| 269. C2 | #14526960 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763163 | 2 |
| C2×#11762604 | 2 |
| #14526960 | 2 |
| C2×C17×#355 | 2 |
| C2×#1414 | 17 |