Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
342 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 113 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. #14545877 | C2 | semidirect |
| 3. C22⋊#10587528 | C2 | semidirect |
| 6. C2×#10587528 | C22 | semidirect |
| 65. C22×D17 | C32 | semidirect |
| 92. C22×C17 | C2×C32 | semidirect |
| 99. C2×D17 | C2×C32 | semidirect |
| 121. D17 | C22⋊C32 | semidirect |
| 142. C17 | C2×C22⋊C32 | semidirect |
| 202. C22 | #11763916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763916 | 2 |
| #14545877 | 2 |
| C22⋊#10587528 | 2 |
| C22×#10587529 | 2 |
| C2×C22⋊C32 | 17 |