Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 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. #14539307 | C2 | semidirect |
| 4. #14526900 | C2 | semidirect |
| 5. #14526899 | C2 | semidirect |
| 6. #14526863 | C2 | semidirect |
| 28. C2×Q16×C17 | Q8 | semidirect |
| 30. C2×D8×C17 | Q8 | semidirect |
| 176. C2×Q16 | Dic34 | semidirect |
| 178. C2×D8 | Dic34 | semidirect |
| 207. C17 | #13373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539307 | 2 |
| #14530520 | 2 |
| #14529678 | 2 |
| #14526900 | 2 |
| #14526899 | 2 |
| #14526863 | 2 |
| C17×#2145 | 2 |
| #13373 | 17 |