Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
892 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 892 conjugacy classes of subgroups — too many to draw. Only its 118 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. #14544675 | C2 | semidirect |
| 2. #14544447 | C2 | semidirect |
| 3. #14543601 | C2 | semidirect |
| 9. #11763675 | C22 | semidirect |
| 10. #11763675 | C22 | semidirect |
| 87. C2×D68 | M16 | semidirect |
| 250. C17 | #7606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544675 | 2 |
| #14544447 | 2 |
| #14543601 | 2 |
| C2×#11762710 | 2 |
| #7606 | 17 |