Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
542 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 180 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. #14543822 | C2 | semidirect |
| 37. C22×C4×C17 | C16 | semidirect |
| 135. C17 | #12844 | semidirect |
| 143. C22×C4 | #63216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#63216 | 2 |
| #14543822 | 2 |
| C22×C4×#3622 | 2 |
| #12844 | 17 |