Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14545946 | C2 | semidirect |
| 4. C2×#11763904 | C2 | semidirect |
| 5. #14545864 | C2 | semidirect |
| 6. #14545859 | C2 | semidirect |
| 9. #11763931 | C4 | semidirect |
| 16. #11763910 | C4 | semidirect |
| 221. C17 | #12615 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763931 | 2 |
| C2×#11763910 | 2 |
| #14545946 | 2 |
| C2×#11763904 | 2 |
| #14545864 | 2 |
| #14545859 | 2 |
| #14544561 | 2 |
| #12615 | 17 |