Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
252 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 63 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×#11762648 | C2 | semidirect |
| 2. C2×#11762647 | C2 | semidirect |
| 3. C2×#11762644 | C2 | semidirect |
| 4. #14531042 | C2 | semidirect |
| 5. #14531032 | C2 | semidirect |
| 6. #14526917 | C2 | semidirect |
| 7. C2×C17×D32 | C2 | semidirect |
| 44. C17×C32 | D4 | semidirect |
| 45. #10587465 | D4 | semidirect |
| 90. C2×D32 | D17 | semidirect |
| 147. C32 | C22⋊D17 | semidirect |
| 148. C17 | #13729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11762648 | 2 |
| C2×#11762647 | 2 |
| C2×#11762644 | 2 |
| #14531042 | 2 |
| #14531032 | 2 |
| #14526917 | 2 |
| C2×C17×D32 | 2 |
| #13729 | 17 |