Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
466 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 120 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. #14545751 | C2 | semidirect |
| 2. #14545026 | C2 | semidirect |
| 3. #14545020 | C2 | semidirect |
| 4. #14543825 | C2 | semidirect |
| 49. C2×#63216 | D4 | semidirect |
| 197. C17 | #12988 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545751 | 2 |
| #14545026 | 2 |
| #14545020 | 2 |
| #14543825 | 2 |
| #14537502 | 2 |
| #12988 | 17 |