Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
218 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 54. #63241 | Q16 | semidirect |
| 57. #63231 | C16 | semidirect |
| 140. C17 | C16×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14546008 | 2 |
| Q8×#63241 | 2 |
| #14545849 | 2 |
| #14545839 | 2 |
| Q8⋊#63241 | 2 |
| C8×#63241 | 2 |
| #14544371 | 2 |
| C16×Q16 | 17 |