Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
270 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 2. #14545867 | C2 | semidirect |
| 3. C4×#10587528 | C2 | semidirect |
| 5. #11763916 | C4 | direct (N × H) |
| 23. #10587528 | C2×C4 | semidirect |
| 50. C4×D17 | C32 | semidirect |
| 65. C4×C17 | C2×C32 | semidirect |
| 69. Dic17 | C2×C32 | semidirect |
| 81. D17 | C4×C32 | semidirect |
| 96. C17 | C2×C4×C32 | semidirect |
| 131. C4 | #11763916 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763916 | 2 |
| #14545867 | 2 |
| C4×#10587528 | 2 |
| C4×#10587529 | 2 |
| C2×C4×C32 | 17 |