Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
386 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 3. #14543744 | C2 | semidirect |
| 23. C2×Q16×C17 | C8 | semidirect |
| 143. C2×Q16 | #3624 | semidirect |
| 168. C17 | #11600 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544990 | 2 |
| #14544331 | 2 |
| #14543744 | 2 |
| C2×Q16×Dic17 | 2 |
| #11600 | 17 |