Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
342 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 9. C4×#63214 | C4 | semidirect |
| 10. C16×Dic17 | C4 | semidirect |
| 11. C4×C16×C17 | C4 | semidirect |
| 90. C4×C16 | #595 | semidirect |
| 111. C17 | #12888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544720 | 2 |
| #14543842 | 2 |
| C4×C16×D17 | 2 |
| #12888 | 17 |