Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
338 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 75 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. #14531007 | C2 | semidirect |
| 2. #14530931 | C2 | semidirect |
| 3. #14528188 | C2 | semidirect |
| 4. #14526830 | C2 | semidirect |
| 5. Q8⋊#63214 | C2 | semidirect |
| 6. #14526745 | C2 | semidirect |
| 187. C17 | #12384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14531007 | 2 |
| #14530931 | 2 |
| #14528188 | 2 |
| #14526830 | 2 |
| Q8⋊#63214 | 2 |
| #14526745 | 2 |
| C17×#3391 | 2 |
| #12384 | 17 |