Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
270 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 149 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. #14545868 | C2 | direct (N × H) |
| 4. #11763916 | C4 | semidirect |
| 6. C2×#10587528 | C4 | semidirect |
| 21. #10587528 | C2×C4 | semidirect |
| 45. C2×#595 | C32 | semidirect |
| 65. #595 | C2×C32 | semidirect |
| 78. C2×C17 | C4×C32 | semidirect |
| 80. D17 | C4×C32 | semidirect |
| 96. C17 | C2×C4×C32 | semidirect |
| 139. C2 | #14545868 | 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 |
| #14545868 | 2 |
| C2×C16×#595 | 2 |
| C2×C4×C32 | 17 |