Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
400 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 3. #14543997 | C2 | semidirect |
| 4. #14543987 | C2 | semidirect |
| 5. #14543624 | C2 | semidirect |
| 6. #14543624 | C2 | semidirect |
| 240. C17 | #8158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544015 | 2 |
| #14543997 | 2 |
| #14543987 | 2 |
| #14543624 | 2 |
| C2×#11762867 | 2 |
| #8158 | 17 |