Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
214 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×#11763916 | C2 | semidirect |
| 2. C4⋊#10587528 | C2 | semidirect |
| 3. #14545877 | C2 | semidirect |
| 4. C4×#10587528 | C2 | semidirect |
| 24. #10587528 | D4 | semidirect |
| 48. D68 | C32 | semidirect |
| 63. C2×D17 | C2×C32 | semidirect |
| 65. C4×C17 | C2×C32 | semidirect |
| 95. C17 | D4×C32 | semidirect |
| 128. C4 | #11763916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763916 | 2 |
| C4⋊#10587528 | 2 |
| #14545877 | 2 |
| C4×#10587528 | 2 |
| #14545163 | 2 |
| D4×C32 | 17 |