Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
508 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 508 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. #14533790 | C2 | semidirect |
| 4. #14526662 | C2 | semidirect |
| 5. #14526651 | C2 | semidirect |
| 6. #14526632 | C2 | semidirect |
| 28. C22×D4×C17 | Q8 | semidirect |
| 37. C2×C4⋊C4×C17 | Q8 | semidirect |
| 258. C22×D4 | Dic34 | semidirect |
| 276. C2×C4⋊C4 | Dic34 | semidirect |
| 298. C17 | #10374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14533790 | 2 |
| #14527352 | 2 |
| C2×#11762543 | 2 |
| #14526662 | 2 |
| #14526651 | 2 |
| #14526632 | 2 |
| C17×#1964 | 2 |
| #10374 | 17 |