Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
242 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 122 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. #14543817 | C2 | semidirect |
| 4. #14543815 | C2 | semidirect |
| 28. C17×M32 | C8 | semidirect |
| 54. C16×C17 | C2×C8 | semidirect |
| 115. M32 | #3624 | semidirect |
| 128. C17 | #12009 | semidirect |
| 148. C16 | C2×#3624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544331 | 2 |
| C2×#11763672 | 2 |
| #14543817 | 2 |
| #14543815 | 2 |
| M32×Dic17 | 2 |
| #12009 | 17 |