Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
470 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 109 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. #14541886 | C2 | semidirect |
| 3. #14530521 | C2 | semidirect |
| 4. #14530519 | C2 | semidirect |
| 5. #14528827 | C2 | semidirect |
| 6. #14526891 | C2 | semidirect |
| 7. C17×#1386 | C2 | semidirect |
| 15. #11763068 | C4 | semidirect |
| 16. #11763063 | C4 | semidirect |
| 53. C17×M32 | D4 | semidirect |
| 62. #10587483 | D4 | semidirect |
| 164. #1386 | D17 | semidirect |
| 237. M32 | D68 | semidirect |
| 250. C17 | #13077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14541886 | 2 |
| #14538447 | 2 |
| #14530521 | 2 |
| #14530519 | 2 |
| #14528827 | 2 |
| #14526891 | 2 |
| C17×#1386 | 2 |
| #13077 | 17 |