Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
520 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 85 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. #14539970 | C2 | semidirect |
| 2. C2×#11763173 | C2 | semidirect |
| 3. #14527498 | C2 | semidirect |
| 4. #14527395 | C2 | semidirect |
| 5. #14527139 | C2 | semidirect |
| 6. #14526684 | C2 | semidirect |
| 256. C17 | #10130 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539970 | 2 |
| C2×#11763173 | 2 |
| #14527498 | 2 |
| #14527395 | 2 |
| #14527139 | 2 |
| #14526684 | 2 |
| C17×#3205 | 2 |
| #10130 | 17 |