Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
538 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 84 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. #14545716 | C2 | semidirect |
| 2. #14544926 | C2 | semidirect |
| 3. #14544291 | C2 | semidirect |
| 4. #14544119 | C2 | semidirect |
| 5. #14543692 | C2 | semidirect |
| 6. #14543668 | C2 | semidirect |
| 157. Q8×C17 | #100 | semidirect |
| 317. C17 | #9360 | semidirect |
| 390. Q8 | #10587553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545716 | 2 |
| #14544926 | 2 |
| #14544291 | 2 |
| #14544119 | 2 |
| #14543692 | 2 |
| #14543668 | 2 |
| #14538262 | 2 |
| #9360 | 17 |