Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
650 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 105 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×#11763247 | C2 | semidirect |
| 2. C2×#11763186 | C2 | semidirect |
| 3. C2×#11762623 | C2 | semidirect |
| 4. #14529672 | C2 | semidirect |
| 5. C17×#1376 | C2 | semidirect |
| 28. C2×Dic68 | D4 | semidirect |
| 40. C2×D136 | D4 | semidirect |
| 45. C17×M32 | D4 | semidirect |
| 130. #1376 | D17 | semidirect |
| 194. M32 | D68 | semidirect |
| 200. C17 | #13331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763247 | 2 |
| C2×#11763186 | 2 |
| C2×#11762623 | 2 |
| #14529672 | 2 |
| C17×#1376 | 2 |
| #13331 | 17 |