Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
744 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 1. C4×#10587545 | C2 | semidirect |
| 3. #14544126 | C2 | semidirect |
| 4. #14544046 | C2 | semidirect |
| 270. C17 | #8368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#10587545 | 2 |
| #14544243 | 2 |
| #14544126 | 2 |
| #14544046 | 2 |
| C2×#11763528 | 2 |
| #8368 | 17 |