Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
554 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 115. Dic68 | Q16 | semidirect |
| 237. C17 | #19931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14541721 | 2 |
| #14541459 | 2 |
| #14528287 | 2 |
| #14528239 | 2 |
| #14528023 | 2 |
| #14527922 | 2 |
| #14527682 | 2 |
| C8×Dic68 | 2 |
| C17×#1707 | 2 |
| #19931 | 17 |