Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
508 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 4. #14526663 | C2 | semidirect |
| 5. #14526651 | C2 | semidirect |
| 6. #14526632 | C2 | semidirect |
| 7. C17×#2549 | C2 | semidirect |
| 31. C22×D68 | Q8 | semidirect |
| 51. C2×C4⋊Dic17 | Q8 | semidirect |
| 186. #2549 | D17 | semidirect |
| 298. C17 | #10374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14529620 | 2 |
| #14527351 | 2 |
| C2×#11762542 | 2 |
| #14526663 | 2 |
| #14526651 | 2 |
| #14526632 | 2 |
| C17×#2549 | 2 |
| #10374 | 17 |