Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
650 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 99 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. #14539704 | C2 | semidirect |
| 2. #14539699 | C2 | semidirect |
| 3. #14539229 | C2 | semidirect |
| 4. #14529607 | C2 | semidirect |
| 5. #14527343 | C2 | semidirect |
| 6. #14526628 | C2 | semidirect |
| 7. C17×#1517 | C2 | semidirect |
| 131. C2×#3622 | D8 | semidirect |
| 185. #1517 | D17 | semidirect |
| 290. C17 | #10218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539704 | 2 |
| #14539699 | 2 |
| #14539229 | 2 |
| #14529607 | 2 |
| #14527343 | 2 |
| #14526628 | 2 |
| C17×#1517 | 2 |
| #10218 | 17 |