Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
350 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 71 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. #14531020 | C2 | semidirect |
| 2. #14530936 | C2 | semidirect |
| 3. #14528297 | C2 | semidirect |
| 4. #14526827 | C2 | semidirect |
| 5. #14526754 | C2 | semidirect |
| 6. #14526742 | C2 | semidirect |
| 80. Q16×C17 | SD16 | semidirect |
| 221. C17 | #12379 | semidirect |
| 240. Q16 | #63229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14531020 | 2 |
| #14530936 | 2 |
| #14528297 | 2 |
| #14526827 | 2 |
| #14526754 | 2 |
| #14526742 | 2 |
| C17×#3277 | 2 |
| #12379 | 17 |