Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
590 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 192 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. #14544397 | C2 | semidirect |
| 68. #63242 | Q16 | semidirect |
| 179. C17 | #17977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545573 | 2 |
| #14544397 | 2 |
| #14544343 | 2 |
| #14544133 | 2 |
| #14543980 | 2 |
| #14539368 | 2 |
| #17977 | 17 |