Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
220 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 66 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. #14544423 | C2 | semidirect |
| 3. #14543815 | C2 | semidirect |
| 4. #14543741 | C2 | semidirect |
| 6. #14543695 | C2 | semidirect |
| 66. C16×C17 | M16 | semidirect |
| 149. C17 | #12084 | semidirect |
| 173. C16 | #63243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544423 | 2 |
| #14544416 | 2 |
| #14543815 | 2 |
| #14543741 | 2 |
| #14543739 | 2 |
| #14543695 | 2 |
| #14530635 | 2 |
| #12084 | 17 |