Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
440 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 40. #10587542 | Q8 | semidirect |
| 180. C17 | #9895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544569 | 2 |
| #14544501 | 2 |
| #14543660 | 2 |
| #14537161 | 2 |
| #9895 | 17 |