Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
360 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 360 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. #14539312 | C2 | semidirect |
| 4. #14526891 | C2 | semidirect |
| 5. #14526886 | C2 | semidirect |
| 6. #14526871 | C2 | semidirect |
| 30. C2×Q16×C17 | Q8 | semidirect |
| 32. C2×D8×C17 | Q8 | semidirect |
| 186. C2×Q16 | Dic34 | semidirect |
| 188. C2×D8 | Dic34 | semidirect |
| 219. C17 | #13374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539312 | 2 |
| #14530520 | 2 |
| #14529683 | 2 |
| #14526891 | 2 |
| #14526886 | 2 |
| #14526871 | 2 |
| C2×C17×#360 | 2 |
| #13374 | 17 |