Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
274 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 55 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. #14531104 | C2 | semidirect |
| 3. C2×#11762649 | C2 | semidirect |
| 4. #14530910 | C2 | semidirect |
| 5. #14526967 | C2 | semidirect |
| 6. #14526927 | C2 | semidirect |
| 7. C17×#1420 | C2 | semidirect |
| 108. #1420 | D17 | semidirect |
| 168. C17 | #13672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14541933 | 2 |
| #14531104 | 2 |
| C2×#11762649 | 2 |
| #14530910 | 2 |
| #14526967 | 2 |
| #14526927 | 2 |
| C17×#1420 | 2 |
| #13672 | 17 |