Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
456 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 88 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. #14544167 | C2 | semidirect |
| 4. #14544133 | C2 | semidirect |
| 5. #14543676 | C2 | semidirect |
| 6. #14543618 | C2 | semidirect |
| 26. #11763104 | C4 | semidirect |
| 27. #11763100 | C4 | semidirect |
| 28. #11763086 | C4 | semidirect |
| 32. C17×#475 | C4 | semidirect |
| 216. #475 | #595 | semidirect |
| 290. C17 | #9209 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545592 | 2 |
| #14544657 | 2 |
| #14544167 | 2 |
| #14544133 | 2 |
| #14543676 | 2 |
| #14543618 | 2 |
| #14538567 | 2 |
| #9209 | 17 |