Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
398 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 55 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. #14536618 | C2 | semidirect |
| 2. #14530005 | C2 | semidirect |
| 4. #14526811 | C2 | semidirect |
| 5. #14526788 | C2 | semidirect |
| 6. #14526729 | C2 | semidirect |
| 7. C17×#1616 | C2 | semidirect |
| 161. #1616 | D17 | semidirect |
| 253. C17 | #12144 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14536618 | 2 |
| #14530005 | 2 |
| #14527719 | 2 |
| #14526811 | 2 |
| #14526788 | 2 |
| #14526729 | 2 |
| C17×#1616 | 2 |
| #12144 | 17 |