Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
378 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. #14527543 | C2 | semidirect |
| 3. #14526746 | C2 | semidirect |
| 4. C2×C4×C16×C17 | C2 | semidirect |
| 105. C2×C4×C16 | D17 | semidirect |
| 170. C17 | #11671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539363 | 2 |
| #14527543 | 2 |
| #14526746 | 2 |
| C2×C4×C16×C17 | 2 |
| #11671 | 17 |