Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
238 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. #14543814 | C2 | semidirect |
| 4. #14543813 | C2 | semidirect |
| 5. #14543807 | C2 | semidirect |
| 6. #14543806 | C2 | semidirect |
| 144. C17 | #12016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545148 | 2 |
| #14545114 | 2 |
| #14543814 | 2 |
| #14543813 | 2 |
| #14543807 | 2 |
| #14543806 | 2 |
| #14527063 | 2 |
| #12016 | 17 |